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diff --git a/docs/htmldoc/mathcomp.ssreflect.bigop.html b/docs/htmldoc/mathcomp.ssreflect.bigop.html deleted file mode 100644 index 97f9fcd..0000000 --- a/docs/htmldoc/mathcomp.ssreflect.bigop.html +++ /dev/null @@ -1,1678 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" -"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> -<html xmlns="http://www.w3.org/1999/xhtml"> -<head> -<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> -<link href="coqdoc.css" rel="stylesheet" type="text/css" /> -<title>mathcomp.ssreflect.bigop</title> -</head> - -<body> - -<div id="page"> - -<div id="header"> -</div> - -<div id="main"> - -<h1 class="libtitle">Library mathcomp.ssreflect.bigop</h1> - -<div class="code"> -<span class="comment">(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. <br/> - Distributed under the terms of CeCILL-B. *)</span><br/> - -<br/> -</div> - -<div class="doc"> - This file provides a generic definition for iterating an operator over a - set of indices (bigop); this big operator is parametrized by the return - type (R), the type of indices (I), the operator (op), the default value on - empty lists (idx), the range of indices (r), the filter applied on this - range (P) and the expression we are iterating (F). The definition is not - to be used directly, but via the wide range of notations provided and - and which support a natural use of big operators. - To improve performance of the Coq typechecker on large expressions, the - bigop constant is OPAQUE. It can however be unlocked to reveal the - transparent constant reducebig, to let Coq expand summation on an explicit - sequence with an explicit test. - The lemmas can be classified according to the operator being iterated: - 1. Results independent of the operator: extensionality with respect to - the range of indices, to the filtering predicate or to the expression - being iterated; reindexing, widening or narrowing of the range of - indices; we provide lemmas for the special cases where indices are - natural numbers or bounded natural numbers ("ordinals"). We supply - several "functional" induction principles that can be used with the - ssreflect 1.3 "elim" tactic to do induction over the index range for - up to 3 bigops simultaneously. - 2. Results depending on the properties of the operator: - We distinguish: monoid laws (op is associative, idx is an identity - element), abelian monoid laws (op is also commutative), and laws with - a distributive operation (semi-rings). Examples of such results are - splitting, permuting, and exchanging bigops. - A special section is dedicated to big operators on natural numbers. -<div class="paragraph"> </div> - - Notations: - The general form for iterated operators is - <bigop>_<range> <general_term> -<ul class="doclist"> -<li> <bigop> is one of \big[op/idx], \sum, \prod, or \max (see below). - -</li> -<li> <general_term> can be any expression. - -</li> -<li> <range> binds an index variable in <general_term>; <range> is one of - (i <- s) i ranges over the sequence s. - (m <= i < n) i ranges over the nat interval m, m+1, ..., n-1. - (i < n) i ranges over the (finite) type 'I_n (i.e., ordinal n). - (i : T) i ranges over the finite type T. - i or (i) i ranges over its (inferred) finite type. - (i in A) i ranges over the elements that satisfy the collective - predicate A (the domain of A must be a finite type). - (i <- s | <condition>) limits the range to the i for which <condition> - holds. <condition> can be any expression that coerces to - bool, and may mention the bound index i. All six kinds of - ranges above can have a <condition> part. - -</li> -<li> One can use the "\big[op/idx]" notations for any operator. - -</li> -<li> BIG_F and BIG_P are pattern abbreviations for the <general_term> and - <condition> part of a \big ... expression; for (i in A) and (i in A | C) - ranges the term matched by BIG_P will include the i \in A condition. - -</li> -<li> The (locked) head constant of a \big notation is bigop. - -</li> -<li> The "\sum", "\prod" and "\max" notations in the %N scope are used for - natural numbers with addition, multiplication and maximum (and their - corresponding neutral elements), respectively. - -</li> -<li> The "\sum" and "\prod" reserved notations are overloaded in ssralg in - the %R scope; in mxalgebra, vector & falgebra in the %MS and %VS scopes; - "\prod" is also overloaded in fingroup, in the %g and %G scopes. - -</li> -<li> We reserve "\bigcup" and "\bigcap" notations for iterated union and - intersection (of sets, groups, vector spaces, etc). -</li> -</ul> - -<div class="paragraph"> </div> - - Tips for using lemmas in this file: - To apply a lemma for a specific operator: if no special property is - required for the operator, simply apply the lemma; if the lemma needs - certain properties for the operator, make sure the appropriate Canonical - instances are declared. -<div class="paragraph"> </div> - - Interfaces for operator properties are packaged in the Monoid submodule: - Monoid.law idx == interface (keyed on the operator) for associative - operators with identity element idx. - Monoid.com_law idx == extension (telescope) of Monoid.law for operators - that are also commutative. - Monoid.mul_law abz == interface for operators with absorbing (zero) - element abz. - Monoid.add_law idx mop == extension of Monoid.com_law for operators over - which operation mop distributes (mop will often also - have a Monoid.mul_law idx structure). - [law of op], [com_law of op], [mul_law of op], [add_law mop of op] == - syntax for cloning Monoid structures. - Monoid.Theory == submodule containing basic generic algebra lemmas - for operators satisfying the Monoid interfaces. - Monoid.simpm == generic monoid simplification rewrite multirule. - Monoid structures are predeclared for many basic operators: (_ && _)%B, - (_ || _)%B, (_ (+) _)%B (exclusive or) , (_ + _)%N, (_ * _)%N, maxn, - gcdn, lcmn and (_ ++ _)%SEQ (list concatenation). -<div class="paragraph"> </div> - - Additional documentation for this file: - Y. Bertot, G. Gonthier, S. Ould Biha and I. Pasca. - Canonical Big Operators. In TPHOLs 2008, LNCS vol. 5170, Springer. - Article available at: - http://hal.inria.fr/docs/00/33/11/93/PDF/main.pdf -<div class="paragraph"> </div> - - Examples of use in: poly.v, matrix.v -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Set Implicit Arguments</span>.<br/> - -<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ i F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0,<br/> - <span class="id" title="tactic">right</span> <span class="id" title="keyword">associativity</span>,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ i '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i <- r | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i <- r | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i <- r ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i <- r ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( m <= i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">m</span>, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( m <= i < n | P ) F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( m <= i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( m <= i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i : t | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i : t | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i : t ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i : t ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i < n ) F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i 'in' A | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i 'in' A | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\big [ op / idx ]_ ( i 'in' A ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">op</span>, <span class="id" title="var">idx</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \big [ op / idx ]_ ( i 'in' A ) '/ ' F ']'").<br/> - -<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ i F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0,<br/> - <span class="id" title="tactic">right</span> <span class="id" title="keyword">associativity</span>,<br/> - <span class="id" title="var">format</span> "'[' \sum_ i '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i <- r | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( i <- r | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i <- r ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( i <- r ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( m <= i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( m <= i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( m <= i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( m <= i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( i | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i : t | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i : t ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i 'in' A | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( i 'in' A | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\sum_ ( i 'in' A ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \sum_ ( i 'in' A ) '/ ' F ']'").<br/> - -<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ i F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0,<br/> - <span class="id" title="var">format</span> "'[' \max_ i '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i <- r | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( i <- r | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i <- r ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( i <- r ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( m <= i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( m <= i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( m <= i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( m <= i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( i | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i : t | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i : t ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( i < n ) F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i 'in' A | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( i 'in' A | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\max_ ( i 'in' A ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \max_ ( i 'in' A ) '/ ' F ']'").<br/> - -<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ i F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0,<br/> - <span class="id" title="var">format</span> "'[' \prod_ i '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i <- r | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( i <- r | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i <- r ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( i <- r ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( m <= i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( m <= i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( m <= i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( m <= i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( i | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i : t | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i : t ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i 'in' A | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( i 'in' A | P ) F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\prod_ ( i 'in' A ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 36, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \prod_ ( i 'in' A ) '/ ' F ']'").<br/> - -<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ i F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ i '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i <- r | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i <- r | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i <- r ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i <- r ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( m <= i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">m</span>, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( m <= i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( m <= i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( m <= i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i : t | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i : t | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i : t ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i : t ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i 'in' A | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i 'in' A | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcup_ ( i 'in' A ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcup_ ( i 'in' A ) '/ ' F ']'").<br/> - -<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ i F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ i '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i <- r | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i <- r | P ) F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i <- r ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">r</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i <- r ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( m <= i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">m</span>, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( m <= i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( m <= i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">m</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( m <= i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i : t | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i : t | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i : t ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i : t ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i < n | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i < n | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i < n ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">n</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i < n ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i 'in' A | P ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i 'in' A | P ) '/ ' F ']'").<br/> -<span class="id" title="keyword">Reserved Notation</span> "\bigcap_ ( i 'in' A ) F"<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">F</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 41, <span class="id" title="var">i</span>, <span class="id" title="var">A</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 50,<br/> - <span class="id" title="var">format</span> "'[' \bigcap_ ( i 'in' A ) '/ ' F ']'").<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="Monoid"><span class="id" title="module">Monoid</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Monoid.Definitions"><span class="id" title="section">Definitions</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="Monoid.Definitions.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Monoid.Definitions.idm"><span class="id" title="variable">idm</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="Monoid.law"><span class="id" title="record">law</span></a> := <a name="Monoid.Law"><span class="id" title="constructor">Law</span></a> {<br/> - <a name="Monoid.operator"><span class="id" title="projection">operator</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#associative"><span class="id" title="definition">associative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#operator"><span class="id" title="method">operator</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#operator"><span class="id" title="method">operator</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_id"><span class="id" title="definition">right_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#operator"><span class="id" title="method">operator</span></a><br/> -}.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="Monoid.com_law"><span class="id" title="record">com_law</span></a> := <a name="Monoid.ComLaw"><span class="id" title="constructor">ComLaw</span></a> {<br/> - <a name="Monoid.com_operator"><span class="id" title="projection">com_operator</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.law"><span class="id" title="record">law</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#com_operator"><span class="id" title="method">com_operator</span></a><br/> -}.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="Monoid.mul_law"><span class="id" title="record">mul_law</span></a> := <a name="Monoid.MulLaw"><span class="id" title="constructor">MulLaw</span></a> {<br/> - <a name="Monoid.mul_operator"><span class="id" title="projection">mul_operator</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_zero"><span class="id" title="definition">left_zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mul_operator"><span class="id" title="method">mul_operator</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_zero"><span class="id" title="definition">right_zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mul_operator"><span class="id" title="method">mul_operator</span></a><br/> -}.<br/> - -<br/> -<span class="id" title="keyword">Structure</span> <a name="Monoid.add_law"><span class="id" title="record">add_law</span></a> (<span class="id" title="var">mul</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a>) := <a name="Monoid.AddLaw"><span class="id" title="constructor">AddLaw</span></a> {<br/> - <a name="Monoid.add_operator"><span class="id" title="projection">add_operator</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">com_law</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_distributive"><span class="id" title="definition">left_distributive</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#add_operator"><span class="id" title="method">add_operator</span></a>;<br/> - <span class="id" title="var">_</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_distributive"><span class="id" title="definition">right_distributive</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#add_operator"><span class="id" title="method">add_operator</span></a><br/> -}.<br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="Monoid.Definitions.op_id"><span class="id" title="variable">op_id</span></a> (<span class="id" title="var">op1</span> <span class="id" title="var">op2</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op1"><span class="id" title="variable">op1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op2"><span class="id" title="variable">op2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="Monoid.clone_law"><span class="id" title="definition">clone_law</span></a> <span class="id" title="var">op</span> :=<br/> - <span class="id" title="keyword">fun</span> (<span class="id" title="var">opL</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.law"><span class="id" title="record">law</span></a>) & <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.op_id"><span class="id" title="variable">op_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opL"><span class="id" title="variable">opL</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">opmA</span> <span class="id" title="var">op1m</span> <span class="id" title="var">opm1</span> (<span class="id" title="var">opL'</span> := @<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opmA"><span class="id" title="variable">opmA</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op1m"><span class="id" title="variable">op1m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opm1"><span class="id" title="variable">opm1</span></a>)<br/> - & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opL'"><span class="id" title="variable">opL'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opL"><span class="id" title="variable">opL</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#opL'"><span class="id" title="variable">opL'</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="Monoid.clone_com_law"><span class="id" title="definition">clone_com_law</span></a> <span class="id" title="var">op</span> :=<br/> - <span class="id" title="keyword">fun</span> (<span class="id" title="var">opL</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.law"><span class="id" title="record">law</span></a>) (<span class="id" title="var">opC</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">com_law</span></a>) & <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.op_id"><span class="id" title="variable">op_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opL"><span class="id" title="variable">opL</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a> & <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.op_id"><span class="id" title="variable">op_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opC"><span class="id" title="variable">opC</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">opmC</span> (<span class="id" title="var">opC'</span> := @<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opL"><span class="id" title="variable">opL</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opmC"><span class="id" title="variable">opmC</span></a>) & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opC'"><span class="id" title="variable">opC'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opC"><span class="id" title="variable">opC</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#opC'"><span class="id" title="variable">opC'</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="Monoid.clone_mul_law"><span class="id" title="definition">clone_mul_law</span></a> <span class="id" title="var">op</span> :=<br/> - <span class="id" title="keyword">fun</span> (<span class="id" title="var">opM</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.mul_law"><span class="id" title="record">mul_law</span></a>) & <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.op_id"><span class="id" title="variable">op_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opM"><span class="id" title="variable">opM</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">op0m</span> <span class="id" title="var">opm0</span> (<span class="id" title="var">opM'</span> := @<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.MulLaw"><span class="id" title="constructor">MulLaw</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#op0m"><span class="id" title="variable">op0m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opm0"><span class="id" title="variable">opm0</span></a>) & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opM'"><span class="id" title="variable">opM'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opM"><span class="id" title="variable">opM</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#opM'"><span class="id" title="variable">opM'</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="Monoid.clone_add_law"><span class="id" title="definition">clone_add_law</span></a> <span class="id" title="var">mop</span> <span class="id" title="var">aop</span> :=<br/> - <span class="id" title="keyword">fun</span> (<span class="id" title="var">opC</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">com_law</span></a>) (<span class="id" title="var">opA</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.add_law"><span class="id" title="record">add_law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mop"><span class="id" title="variable">mop</span></a>) & <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.op_id"><span class="id" title="variable">op_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opC"><span class="id" title="variable">opC</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#aop"><span class="id" title="variable">aop</span></a> & <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions.op_id"><span class="id" title="variable">op_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opA"><span class="id" title="variable">opA</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#aop"><span class="id" title="variable">aop</span></a> ⇒<br/> - <span class="id" title="keyword">fun</span> <span class="id" title="var">mopDm</span> <span class="id" title="var">mopmD</span> (<span class="id" title="var">opA'</span> := @<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mop"><span class="id" title="variable">mop</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opC"><span class="id" title="variable">opC</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mopDm"><span class="id" title="variable">mopDm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mopmD"><span class="id" title="variable">mopmD</span></a>)<br/> - & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#phant_id"><span class="id" title="definition">phant_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opA'"><span class="id" title="variable">opA'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#opA"><span class="id" title="variable">opA</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#opA'"><span class="id" title="variable">opA'</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Definitions"><span class="id" title="section">Definitions</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Import</span> <a name="Monoid.Exports"><span class="id" title="module">Exports</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.operator"><span class="id" title="projection">operator</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.operator"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.operator"><span class="id" title="projection">law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.operator"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.operator"><span class="id" title="projection">Funclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_operator"><span class="id" title="projection">com_operator</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_operator"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_operator"><span class="id" title="projection">com_law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_operator"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_operator"><span class="id" title="projection">law</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.mul_operator"><span class="id" title="projection">mul_operator</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.mul_operator"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.mul_operator"><span class="id" title="projection">mul_law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.mul_operator"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.mul_operator"><span class="id" title="projection">Funclass</span></a>.<br/> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.add_operator"><span class="id" title="projection">add_operator</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.add_operator"><span class="id" title="projection">:</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.add_operator"><span class="id" title="projection">add_law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.add_operator"><span class="id" title="projection">>-></span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.add_operator"><span class="id" title="projection">com_law</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c0ead7c536b771c2de27837c46f4d177"><span class="id" title="notation">"</span></a>[ 'law' 'of' f ]" := (@<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.clone_law"><span class="id" title="definition">clone_law</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">f</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span>"[ 'law' 'of' f ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="f6879cc6b2f76829a745ea8ba8f8ac82"><span class="id" title="notation">"</span></a>[ 'com_law' 'of' f ]" := (@<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.clone_com_law"><span class="id" title="definition">clone_com_law</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">f</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'com_law' 'of' f ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c8301b47409c0354edf11a5fa45f684e"><span class="id" title="notation">"</span></a>[ 'mul_law' 'of' f ]" := (@<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.clone_mul_law"><span class="id" title="definition">clone_mul_law</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">f</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span>"[ 'mul_law' 'of' f ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="9817ef3828fb82ac1e3d0b86f80b4caa"><span class="id" title="notation">"</span></a>[ 'add_law' m 'of' a ]" := (@<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.clone_add_law"><span class="id" title="definition">clone_add_law</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">m</span> <span class="id" title="var">a</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#id"><span class="id" title="abbreviation">id</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'add_law' m 'of' a ]") : <span class="id" title="var">form_scope</span>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Exports"><span class="id" title="module">Exports</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Monoid.CommutativeAxioms"><span class="id" title="section">CommutativeAxioms</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> (<a name="Monoid.CommutativeAxioms.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Monoid.CommutativeAxioms.zero"><span class="id" title="variable">zero</span></a> <a name="Monoid.CommutativeAxioms.one"><span class="id" title="variable">one</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>) (<a name="Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a> <a name="Monoid.CommutativeAxioms.add"><span class="id" title="variable">add</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>) (<a name="Monoid.CommutativeAxioms.inv"><span class="id" title="variable">inv</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Monoid.CommutativeAxioms.mulC"><span class="id" title="variable">mulC</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.mulC_id"><span class="id" title="lemma">mulC_id</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.one"><span class="id" title="variable">one</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_id"><span class="id" title="definition">right_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.one"><span class="id" title="variable">one</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.mulC_zero"><span class="id" title="lemma">mulC_zero</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_zero"><span class="id" title="definition">left_zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.zero"><span class="id" title="variable">zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_zero"><span class="id" title="definition">right_zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.zero"><span class="id" title="variable">zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.mulC_dist"><span class="id" title="lemma">mulC_dist</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_distributive"><span class="id" title="definition">left_distributive</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.add"><span class="id" title="variable">add</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_distributive"><span class="id" title="definition">right_distributive</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms.add"><span class="id" title="variable">add</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.CommutativeAxioms"><span class="id" title="section">CommutativeAxioms</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="Monoid.Theory"><span class="id" title="module">Theory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Monoid.Theory.Theory"><span class="id" title="section">Theory</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="Monoid.Theory.Theory.T"><span class="id" title="variable">T</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Monoid.Theory.Theory.Plain"><span class="id" title="section">Plain</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="Monoid.Theory.Theory.Plain.mul"><span class="id" title="variable">mul</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.law"><span class="id" title="record">law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mul1m"><span class="id" title="lemma">mul1m</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Plain.mul"><span class="id" title="variable">mul</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulm1"><span class="id" title="lemma">mulm1</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_id"><span class="id" title="definition">right_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Plain.mul"><span class="id" title="variable">mul</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulmA"><span class="id" title="lemma">mulmA</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#associative"><span class="id" title="definition">associative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Plain.mul"><span class="id" title="variable">mul</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.iteropE"><span class="id" title="lemma">iteropE</span></a> <span class="id" title="var">n</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iterop"><span class="id" title="definition">iterop</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Plain.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Plain.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a>.<br/> - <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Plain"><span class="id" title="section">Plain</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Monoid.Theory.Theory.Commutative"><span class="id" title="section">Commutative</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="Monoid.Theory.Theory.Commutative.mul"><span class="id" title="variable">mul</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">com_law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulmC"><span class="id" title="lemma">mulmC</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Commutative.mul"><span class="id" title="variable">mul</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulmCA"><span class="id" title="lemma">mulmCA</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_commutative"><span class="id" title="definition">left_commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Commutative.mul"><span class="id" title="variable">mul</span></a>.<br/> - <span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulmAC"><span class="id" title="lemma">mulmAC</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_commutative"><span class="id" title="definition">right_commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Commutative.mul"><span class="id" title="variable">mul</span></a>.<br/> - <span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulmACA"><span class="id" title="lemma">mulmACA</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#interchange"><span class="id" title="definition">interchange</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Commutative.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Commutative.mul"><span class="id" title="variable">mul</span></a>.<br/> - <span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Commutative"><span class="id" title="section">Commutative</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Monoid.Theory.Theory.Mul"><span class="id" title="section">Mul</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="Monoid.Theory.Theory.Mul.mul"><span class="id" title="variable">mul</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.mul_law"><span class="id" title="record">mul_law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mul0m"><span class="id" title="lemma">mul0m</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_zero"><span class="id" title="definition">left_zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Mul.mul"><span class="id" title="variable">mul</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulm0"><span class="id" title="lemma">mulm0</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_zero"><span class="id" title="definition">right_zero</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Mul.mul"><span class="id" title="variable">mul</span></a>. <br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Mul"><span class="id" title="section">Mul</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Monoid.Theory.Theory.Add"><span class="id" title="section">Add</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="Monoid.Theory.Theory.Add.mul"><span class="id" title="variable">mul</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.T"><span class="id" title="variable">T</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.T"><span class="id" title="variable">T</span></a>) (<a name="Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.add_law"><span class="id" title="record">add_law</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#mul"><span class="id" title="variable">mul</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.addmA"><span class="id" title="lemma">addmA</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#associative"><span class="id" title="definition">associative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.addmC"><span class="id" title="lemma">addmC</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#commutative"><span class="id" title="definition">commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.addmCA"><span class="id" title="lemma">addmCA</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_commutative"><span class="id" title="definition">left_commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.addmAC"><span class="id" title="lemma">addmAC</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_commutative"><span class="id" title="definition">right_commutative</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.add0m"><span class="id" title="lemma">add0m</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_id"><span class="id" title="definition">left_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.addm0"><span class="id" title="lemma">addm0</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_id"><span class="id" title="definition">right_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.idm"><span class="id" title="variable">idm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulm_addl"><span class="id" title="lemma">mulm_addl</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#left_distributive"><span class="id" title="definition">left_distributive</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Monoid.Theory.mulm_addr"><span class="id" title="lemma">mulm_addr</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_distributive"><span class="id" title="definition">right_distributive</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.mul"><span class="id" title="variable">mul</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add.add"><span class="id" title="variable">add</span></a>. <br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory.Add"><span class="id" title="section">Add</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="Monoid.Theory.simpm"><span class="id" title="definition">simpm</span></a> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.mulm1"><span class="id" title="lemma">mulm1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.mulm0"><span class="id" title="lemma">mulm0</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.mul1m"><span class="id" title="lemma">mul1m</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.mul0m"><span class="id" title="lemma">mul0m</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.mulmA"><span class="id" title="lemma">mulmA</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory.Theory"><span class="id" title="section">Theory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory"><span class="id" title="module">Theory</span></a>.<br/> -<span class="id" title="keyword">Include</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.Theory"><span class="id" title="module">Theory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid"><span class="id" title="module">Monoid</span></a>.<br/> -<span class="id" title="keyword">Export</span> <span class="id" title="var">Monoid.Exports</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="PervasiveMonoids"><span class="id" title="section">PervasiveMonoids</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Monoid</span>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">andb_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andbA"><span class="id" title="lemma">andbA</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andTb"><span class="id" title="lemma">andTb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andbT"><span class="id" title="lemma">andbT</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">andb_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andbC"><span class="id" title="lemma">andbC</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">andb_muloid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#MulLaw"><span class="id" title="constructor">MulLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andFb"><span class="id" title="lemma">andFb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andbF"><span class="id" title="lemma">andbF</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">orb_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orbA"><span class="id" title="lemma">orbA</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orFb"><span class="id" title="lemma">orFb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orbF"><span class="id" title="lemma">orbF</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">orb_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orbC"><span class="id" title="lemma">orbC</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">orb_muloid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#MulLaw"><span class="id" title="constructor">MulLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orTb"><span class="id" title="lemma">orTb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orbT"><span class="id" title="lemma">orbT</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">addb_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#addbA"><span class="id" title="lemma">addbA</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#addFb"><span class="id" title="lemma">addFb</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#addbF"><span class="id" title="lemma">addbF</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">addb_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#addbC"><span class="id" title="lemma">addbC</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">orb_addoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andb_orl"><span class="id" title="lemma">andb_orl</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andb_orr"><span class="id" title="lemma">andb_orr</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">andb_addoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orb_andl"><span class="id" title="lemma">orb_andl</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#orb_andr"><span class="id" title="lemma">orb_andr</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">addb_addoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andb_addl"><span class="id" title="lemma">andb_addl</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#andb_addr"><span class="id" title="lemma">andb_addr</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">addn_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#addnA"><span class="id" title="lemma">addnA</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#add0n"><span class="id" title="lemma">add0n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#addn0"><span class="id" title="lemma">addn0</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">addn_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#addnC"><span class="id" title="lemma">addnC</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">muln_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#mulnA"><span class="id" title="lemma">mulnA</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#mul1n"><span class="id" title="lemma">mul1n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#muln1"><span class="id" title="lemma">muln1</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">muln_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#mulnC"><span class="id" title="lemma">mulnC</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">muln_muloid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#MulLaw"><span class="id" title="constructor">MulLaw</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#mul0n"><span class="id" title="lemma">mul0n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#muln0"><span class="id" title="lemma">muln0</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">addn_addoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#mulnDl"><span class="id" title="lemma">mulnDl</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#mulnDr"><span class="id" title="lemma">mulnDr</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">maxn_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxnA"><span class="id" title="lemma">maxnA</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#max0n"><span class="id" title="lemma">max0n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn0"><span class="id" title="lemma">maxn0</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">maxn_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxnC"><span class="id" title="lemma">maxnC</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">maxn_addoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn_mull"><span class="id" title="lemma">maxn_mull</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn_mulr"><span class="id" title="lemma">maxn_mulr</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">gcdn_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#gcdnA"><span class="id" title="lemma">gcdnA</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#gcd0n"><span class="id" title="lemma">gcd0n</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#gcdn0"><span class="id" title="lemma">gcdn0</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">gcdn_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#gcdnC"><span class="id" title="lemma">gcdnC</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">gcdnDoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#muln_gcdl"><span class="id" title="lemma">muln_gcdl</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#muln_gcdr"><span class="id" title="lemma">muln_gcdr</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lcmn_monoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#lcmnA"><span class="id" title="lemma">lcmnA</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#lcm1n"><span class="id" title="lemma">lcm1n</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#lcmn1"><span class="id" title="lemma">lcmn1</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lcmn_comoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#ComLaw"><span class="id" title="constructor">ComLaw</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#lcmnC"><span class="id" title="lemma">lcmnC</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">lcmn_addoid</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#AddLaw"><span class="id" title="constructor">AddLaw</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#muln_lcml"><span class="id" title="lemma">muln_lcml</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#muln_lcmr"><span class="id" title="lemma">muln_lcmr</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">cat_monoid</span> <span class="id" title="var">T</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#Law"><span class="id" title="constructor">Law</span></a> (@<a class="idref" href="mathcomp.ssreflect.seq.html#catA"><span class="id" title="lemma">catA</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.seq.html#cat0s"><span class="id" title="lemma">cat0s</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.seq.html#cats0"><span class="id" title="lemma">cats0</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#PervasiveMonoids"><span class="id" title="section">PervasiveMonoids</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Unit test for the [...law of ... ] Notations -Definition myp := addn. Definition mym := muln. -Canonical myp_mon := [law of myp]. -Canonical myp_cmon := [com_law of myp]. -Canonical mym_mul := [mul_law of mym]. -Canonical myp_add := [add_law _ of myp]. -Print myp_add. -Print Canonical Projections. - -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Delimit</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">big_scope</span> <span class="id" title="keyword">with</span> <span class="id" title="var">BIG</span>.<br/> -<span class="id" title="keyword">Open</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">big_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - The bigbody wrapper is a workaround for a quirk of the Coq pretty-printer, - which would fail to redisplay the \big notation when the <general_term> or - <condition> do not depend on the bound index. The BigBody constructor - packages both in in a term in which i occurs; it also depends on the - iterated <op>, as this can give more information on the expected type of - the <general_term>, thus allowing for the insertion of coercions. -</div> -<div class="code"> -<span class="id" title="keyword">Variant</span> <a name="bigbody"><span class="id" title="inductive">bigbody</span></a> <span class="id" title="var">R</span> <span class="id" title="var">I</span> := <a name="BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> & (<a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a>) & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#bool"><span class="id" title="inductive">bool</span></a> & <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="applybig"><span class="id" title="definition">applybig</span></a> {<span class="id" title="var">R</span> <span class="id" title="var">I</span>} (<span class="id" title="var">body</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#bigbody"><span class="id" title="inductive">bigbody</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">x</span> :=<br/> - <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">_</span> <span class="id" title="var">op</span> <span class="id" title="var">b</span> <span class="id" title="var">v</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#body"><span class="id" title="variable">body</span></a> <span class="id" title="tactic">in</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <span class="id" title="var">b</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <span class="id" title="var">op</span> <span class="id" title="var">v</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="reducebig"><span class="id" title="definition">reducebig</span></a> <span class="id" title="var">R</span> <span class="id" title="var">I</span> <span class="id" title="var">idx</span> <span class="id" title="var">r</span> (<span class="id" title="var">body</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#bigbody"><span class="id" title="inductive">bigbody</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) :=<br/> - <a class="idref" href="mathcomp.ssreflect.seq.html#foldr"><span class="id" title="definition">foldr</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#applybig"><span class="id" title="definition">applybig</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8b4742e3f67816503ce4ab2f3b81c27e"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#8b4742e3f67816503ce4ab2f3b81c27e"><span class="id" title="notation">o</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#body"><span class="id" title="variable">body</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#idx"><span class="id" title="variable">idx</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Type</span> <a name="BigOpSig"><span class="id" title="module">BigOpSig</span></a>.<br/> -<span class="id" title="keyword">Parameter</span> <a name="BigOpSig.bigop"><span class="id" title="axiom">bigop</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">R</span> <span class="id" title="var">I</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#bigbody"><span class="id" title="inductive">bigbody</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a>.<br/> -<span class="id" title="keyword">Axiom</span> <a name="BigOpSig.bigopE"><span class="id" title="axiom">bigopE</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#BigOpSig.bigop"><span class="id" title="axiom">bigop</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#reducebig"><span class="id" title="definition">reducebig</span></a>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigOpSig"><span class="id" title="module">BigOpSig</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="BigOp"><span class="id" title="module">BigOp</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#BigOpSig"><span class="id" title="module">BigOpSig</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="BigOp.bigop"><span class="id" title="definition">bigop</span></a> := <a class="idref" href="mathcomp.ssreflect.bigop.html#reducebig"><span class="id" title="definition">reducebig</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="BigOp.bigopE"><span class="id" title="lemma">bigopE</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#BigOp.bigop"><span class="id" title="definition">bigop</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#reducebig"><span class="id" title="definition">reducebig</span></a>. <br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigOp"><span class="id" title="module">BigOp</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="bigop"><span class="id" title="abbreviation">bigop</span></a> := <a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="axiom">BigOp.bigop</span></a> (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">bigop_unlock</span> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Unlockable"><span class="id" title="constructor">Unlockable</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#bigopE"><span class="id" title="axiom">BigOp.bigopE</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="index_iota"><span class="id" title="definition">index_iota</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> := <a class="idref" href="mathcomp.ssreflect.seq.html#iota"><span class="id" title="definition">iota</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7825ccc99f23b0d30c9d40c317ba7af0"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="index_enum"><span class="id" title="definition">index_enum</span></a> (<span class="id" title="var">T</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) := <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.enum"><span class="id" title="abbreviation">Finite.enum</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="mem_index_iota"><span class="id" title="lemma">mem_index_iota</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#index_iota"><span class="id" title="definition">index_iota</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="mem_index_enum"><span class="id" title="lemma">mem_index_enum</span></a> <span class="id" title="var">T</span> <span class="id" title="var">i</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#index_enum"><span class="id" title="definition">index_enum</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>.<br/> - <span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">mem_index_enum</span> : <span class="id" title="var">core</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="filter_index_enum"><span class="id" title="lemma">filter_index_enum</span></a> <span class="id" title="var">T</span> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#filter"><span class="id" title="definition">filter</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#index_enum"><span class="id" title="definition">index_enum</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#T"><span class="id" title="variable">T</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#enum"><span class="id" title="abbreviation">enum</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( i <- r | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> <span class="id" title="var">r</span> (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <span class="id" title="var">P</span>%<span class="id" title="var">B</span> <span class="id" title="var">F</span>)) : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( i <- r ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> <span class="id" title="var">r</span> (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <span class="id" title="var">F</span>)) : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( m <= i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> (<a class="idref" href="mathcomp.ssreflect.bigop.html#index_iota"><span class="id" title="definition">index_iota</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <span class="id" title="var">P</span>%<span class="id" title="var">B</span> <span class="id" title="var">F</span>))<br/> - : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( m <= i < n ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> (<a class="idref" href="mathcomp.ssreflect.bigop.html#index_iota"><span class="id" title="definition">index_iota</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <span class="id" title="var">F</span>))<br/> - : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="1871917561e26284874cb982a8cc32df"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( i | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> (<a class="idref" href="mathcomp.ssreflect.bigop.html#index_enum"><span class="id" title="definition">index_enum</span></a> <span class="id" title="var">_</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <span class="id" title="var">P</span>%<span class="id" title="var">B</span> <span class="id" title="var">F</span>)) : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ i F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> (<a class="idref" href="mathcomp.ssreflect.bigop.html#index_enum"><span class="id" title="definition">index_enum</span></a> <span class="id" title="var">_</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <span class="id" title="var">F</span>)) : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( i : t | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> (<a class="idref" href="mathcomp.ssreflect.bigop.html#index_enum"><span class="id" title="definition">index_enum</span></a> <span class="id" title="var">_</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> : <span class="id" title="var">t</span> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <span class="id" title="var">P</span>%<span class="id" title="var">B</span> <span class="id" title="var">F</span>))<br/> - (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( i : t ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#bigop"><span class="id" title="abbreviation">bigop</span></a> <span class="id" title="var">idx</span> (<a class="idref" href="mathcomp.ssreflect.bigop.html#index_enum"><span class="id" title="definition">index_enum</span></a> <span class="id" title="var">_</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">i</span> : <span class="id" title="var">t</span> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBody"><span class="id" title="constructor">BigBody</span></a> <span class="id" title="var">i</span> <span class="id" title="var">op</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a> <span class="id" title="var">F</span>))<br/> - (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">big_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">"</span></a>\big [ op / idx ]_ ( i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">[</span></a><span class="id" title="var">op</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">/</span></a><span class="id" title="var">idx</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ordinal"><span class="id" 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title="notation">[</span></a><span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <span class="id" 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href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssrmatching.ssrmatching.html#948ad4812b0da96c499e137b53f76d02"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span 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href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssrmatching.ssrmatching.html#948ad4812b0da96c499e137b53f76d02"><span class="id" title="notation">)</span></a>%<span class="id" title="tactic">pattern</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">"</span></a>\sum_ ( i <- r | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" 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class="id" title="var">r</span><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3ce1c301339a15a6afaadd0cff38b67a"><span class="id" title="notation">"</span></a>\sum_ ( m <= i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><span class="id" title="var">m</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c0980ea1654f471922ad26f5837d48da"><span class="id" title="notation">"</span></a>\sum_ ( m <= i < n ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><span class="id" title="var">m</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="490a7188a07350a81d958e0206419577"><span class="id" title="notation">"</span></a>\sum_ ( i | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="e903f8dba09838168c567661c1b86640"><span class="id" title="notation">"</span></a>\sum_ i F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="78b74f6262fe48daecc324b45008080d"><span class="id" title="notation">"</span></a>\sum_ ( i : t | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">:</span></a> <span class="id" title="var">t</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="df583ad63596ccb0876c752cdeaa2b71"><span class="id" title="notation">"</span></a>\sum_ ( i : t ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">:</span></a> <span class="id" title="var">t</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="022fb0cf06ab932b1bc4ba1bc95dac17"><span class="id" title="notation">"</span></a>\sum_ ( i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="e383fcd76deb34dd09a423262c4c7429"><span class="id" title="notation">"</span></a>\sum_ ( i < n ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d3f1e190d1bbbe6d01fc5164e016dfaa"><span class="id" title="notation">"</span></a>\sum_ ( i 'in' A | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">"</span></a>\sum_ ( i 'in' A ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#32140f70a8dca915a2dcc40e6207ec4c"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">"</span></a>\prod_ ( i <- r | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <span class="id" title="var">r</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a45c0ee2d529b0e12bd021f95ea69ebb"><span class="id" title="notation">"</span></a>\prod_ ( i <- r ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <span class="id" title="var">r</span><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="5104cf97537506dbca0e1221c0a609c2"><span class="id" title="notation">"</span></a>\prod_ ( m <= i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><span class="id" title="var">m</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="b46f4e825b398c0eb860f658bff447f6"><span class="id" title="notation">"</span></a>\prod_ ( m <= i < n ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><span class="id" title="var">m</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="e6d2fd31a18db752798c29ac9a032fd2"><span class="id" title="notation">"</span></a>\prod_ ( i | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="5a9af0620b1b0f6a8f15144a68113105"><span class="id" title="notation">"</span></a>\prod_ i F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="af0245b6e3dc9a4f2f039548d71e757b"><span class="id" title="notation">"</span></a>\prod_ ( i : t | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">:</span></a> <span class="id" title="var">t</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="7b1df3fcb5203c74fc358bfca00e70a3"><span class="id" title="notation">"</span></a>\prod_ ( i : t ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">:</span></a> <span class="id" title="var">t</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="401a74983115c4f3f187bf75c790604f"><span class="id" title="notation">"</span></a>\prod_ ( i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a123b1dc36c336b1513d2ed357840b93"><span class="id" title="notation">"</span></a>\prod_ ( i < n ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="716ae637eff9703ca2c2067d28556c85"><span class="id" title="notation">"</span></a>\prod_ ( i 'in' A | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="2e5c92af4bc9a12f0e6a46802637177b"><span class="id" title="notation">"</span></a>\prod_ ( i 'in' A ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#495b239647dbf627c667bea21e9cedf0"><span class="id" title="notation">N</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="8973d8916b0a092278944d6bb0b02462"><span class="id" title="notation">"</span></a>\max_ ( i <- r | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <span class="id" title="var">r</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="14bf6b825fa7c225eab7220105f1e946"><span class="id" title="notation">"</span></a>\max_ ( i <- r ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <span class="id" title="var">r</span><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">"</span></a>\max_ ( i | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d7221eb7e755bf25abb3156848a10d4b"><span class="id" title="notation">"</span></a>\max_ i F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="fd771f30a6bfe698b66120cda6fc4b42"><span class="id" title="notation">"</span></a>\max_ ( i : I | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">:</span></a> <span class="id" title="var">I</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d29fb863c8a94180218167e618d20ffb"><span class="id" title="notation">"</span></a>\max_ ( i : I ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">:</span></a> <span class="id" title="var">I</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="cb788ef57c2f030fba53975aa2da99f0"><span class="id" title="notation">"</span></a>\max_ ( m <= i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><span class="id" title="var">m</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a17f5f325fb114ca17db732e2418a0ad"><span class="id" title="notation">"</span></a>\max_ ( m <= i < n ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><span class="id" title="var">m</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="0067c9a63bbc9c19a08e88ede5f42fbe"><span class="id" title="notation">"</span></a>\max_ ( i < n | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3a447b0afd9ad8298064c27788129338"><span class="id" title="notation">"</span></a>\max_ ( i < n ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <span class="id" title="var">n</span><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="7b049b5e134c54343818c497d8df1485"><span class="id" title="notation">"</span></a>\max_ ( i 'in' A | P ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span>%<span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="ec60518d5ab0e853ea27ade01a2f345b"><span class="id" title="notation">"</span></a>\max_ ( i 'in' A ) F" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#maxn"><span class="id" title="definition">maxn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <span class="id" title="var">F</span>%<span class="id" title="var">N</span>) : <span class="id" title="var">nat_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - Induction loading -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="big_load"><span class="id" title="lemma">big_load</span></a> <span class="id" title="var">R</span> (<span class="id" title="var">K</span> <span class="id" title="var">K'</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Type</span>) <span class="id" title="var">idx</span> <span class="id" title="var">op</span> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#11c698c8685bb8ab1cf725545c085ac4"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#K'"><span class="id" title="variable">K'</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#K'"><span class="id" title="variable">K'</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Elim3"><span class="id" title="section">Elim3</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim3.R1"><span class="id" title="variable">R1</span></a> <a name="Elim3.R2"><span class="id" title="variable">R2</span></a> <a name="Elim3.R3"><span class="id" title="variable">R3</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Elim3.K"><span class="id" title="variable">K</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R3"><span class="id" title="variable">R3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Type</span>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim3.id1"><span class="id" title="variable">id1</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R1"><span class="id" title="variable">R1</span></a>) (<a name="Elim3.op1"><span class="id" title="variable">op1</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R1"><span class="id" title="variable">R1</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim3.id2"><span class="id" title="variable">id2</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R2"><span class="id" title="variable">R2</span></a>) (<a name="Elim3.op2"><span class="id" title="variable">op2</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R2"><span class="id" title="variable">R2</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim3.id3"><span class="id" title="variable">id3</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R3"><span class="id" title="variable">R3</span></a>) (<a name="Elim3.op3"><span class="id" title="variable">op3</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R3"><span class="id" title="variable">R3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R3"><span class="id" title="variable">R3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.R3"><span class="id" title="variable">R3</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Elim3.Kid"><span class="id" title="variable">Kid</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id1"><span class="id" title="variable">id1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id2"><span class="id" title="variable">id2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id3"><span class="id" title="variable">id3</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_rec3"><span class="id" title="lemma">big_rec3</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> <span class="id" title="var">F3</span><br/> - (<span class="id" title="var">K_F</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span> <span class="id" title="var">y1</span> <span class="id" title="var">y2</span> <span class="id" title="var">y3</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y3"><span class="id" title="variable">y3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op1"><span class="id" title="variable">op1</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op2"><span class="id" title="variable">op2</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op3"><span class="id" title="variable">op3</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F3"><span class="id" title="variable">F3</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#y3"><span class="id" title="variable">y3</span></a>)) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op1"><span class="id" title="variable">op1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id1"><span class="id" title="variable">id1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op2"><span class="id" title="variable">op2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id2"><span class="id" title="variable">id2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op3"><span class="id" title="variable">op3</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id3"><span class="id" title="variable">id3</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F3"><span class="id" title="variable">F3</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Elim3.Kop"><span class="id" title="variable">Kop</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x1</span> <span class="id" title="var">x2</span> <span class="id" title="var">x3</span> <span class="id" title="var">y1</span> <span class="id" title="var">y2</span> <span class="id" title="var">y3</span>,<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x2"><span class="id" title="variable">x2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x3"><span class="id" title="variable">x3</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y3"><span class="id" title="variable">y3</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op1"><span class="id" title="variable">op1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op2"><span class="id" title="variable">op2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x2"><span class="id" title="variable">x2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op3"><span class="id" title="variable">op3</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x3"><span class="id" title="variable">x3</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y3"><span class="id" title="variable">y3</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ind3"><span class="id" title="lemma">big_ind3</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> <span class="id" title="var">F3</span><br/> - (<span class="id" title="var">K_F</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#F3"><span class="id" title="variable">F3</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op1"><span class="id" title="variable">op1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id1"><span class="id" title="variable">id1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op2"><span class="id" title="variable">op2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id2"><span class="id" title="variable">id2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.op3"><span class="id" title="variable">op3</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3.id3"><span class="id" title="variable">id3</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F3"><span class="id" title="variable">F3</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim3"><span class="id" title="section">Elim3</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Elim2"><span class="id" title="section">Elim2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim2.R1"><span class="id" title="variable">R1</span></a> <a name="Elim2.R2"><span class="id" title="variable">R2</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Elim2.K"><span class="id" title="variable">K</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Type</span>) (<a name="Elim2.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R1"><span class="id" title="variable">R1</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim2.id1"><span class="id" title="variable">id1</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R1"><span class="id" title="variable">R1</span></a>) (<a name="Elim2.op1"><span class="id" title="variable">op1</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R1"><span class="id" title="variable">R1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R1"><span class="id" title="variable">R1</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim2.id2"><span class="id" title="variable">id2</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R2"><span class="id" title="variable">R2</span></a>) (<a name="Elim2.op2"><span class="id" title="variable">op2</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R2"><span class="id" title="variable">R2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.R2"><span class="id" title="variable">R2</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Elim2.Kid"><span class="id" title="variable">Kid</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id1"><span class="id" title="variable">id1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id2"><span class="id" title="variable">id2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_rec2"><span class="id" title="lemma">big_rec2</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span><br/> - (<span class="id" title="var">K_F</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span> <span class="id" title="var">y1</span> <span class="id" title="var">y2</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op1"><span class="id" title="variable">op1</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op2"><span class="id" title="variable">op2</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a>)) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op1"><span class="id" title="variable">op1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id1"><span class="id" title="variable">id1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op2"><span class="id" title="variable">op2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id2"><span class="id" title="variable">id2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Elim2.Kop"><span class="id" title="variable">Kop</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x1</span> <span class="id" title="var">x2</span> <span class="id" title="var">y1</span> <span class="id" title="var">y2</span>,<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x2"><span class="id" title="variable">x2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op1"><span class="id" title="variable">op1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y1"><span class="id" title="variable">y1</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op2"><span class="id" title="variable">op2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x2"><span class="id" title="variable">x2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y2"><span class="id" title="variable">y2</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ind2"><span class="id" title="lemma">big_ind2</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> (<span class="id" title="var">K_F</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op1"><span class="id" title="variable">op1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id1"><span class="id" title="variable">id1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op2"><span class="id" title="variable">op2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id2"><span class="id" title="variable">id2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="Elim2.f_op"><span class="id" title="variable">f_op</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op2"><span class="id" title="variable">op2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">>-></span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op1"><span class="id" title="variable">op1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#40d800f6f36c47cb5f4f2f42555867a8"><span class="id" title="notation">}</span></a>) (<a name="Elim2.f_id"><span class="id" title="variable">f_id</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id2"><span class="id" title="variable">id2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id1"><span class="id" title="variable">id1</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_morph"><span class="id" title="lemma">big_morph</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op2"><span class="id" title="variable">op2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id2"><span class="id" title="variable">id2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.op1"><span class="id" title="variable">op1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.id1"><span class="id" title="variable">id1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2.f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim2"><span class="id" title="section">Elim2</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Elim1"><span class="id" title="section">Elim1</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim1.R"><span class="id" title="variable">R</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Elim1.K"><span class="id" title="variable">K</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Type</span>) (<a name="Elim1.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="Elim1.idx"><span class="id" title="variable">idx</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.R"><span class="id" title="variable">R</span></a>) (<a name="Elim1.op"><span class="id" title="variable">op</span></a> <a name="Elim1.op'"><span class="id" title="variable">op'</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.R"><span class="id" title="variable">R</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Elim1.Kid"><span class="id" title="variable">Kid</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_rec"><span class="id" title="lemma">big_rec</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span><br/> - (<span class="id" title="var">Kop</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span> <span class="id" title="var">x</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>)) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Elim1.Kop"><span class="id" title="variable">Kop</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ind"><span class="id" title="lemma">big_ind</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> (<span class="id" title="var">K_F</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Elim1.Kop'"><span class="id" title="variable">Kop'</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op'"><span class="id" title="variable">op'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_big_op"><span class="id" title="lemma">eq_big_op</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> (<span class="id" title="var">K_F</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.K"><span class="id" title="variable">K</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op'"><span class="id" title="variable">op'</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Hypotheses</span> (<a name="Elim1.fM"><span class="id" title="variable">fM</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">morph</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.f"><span class="id" title="variable">f</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">:</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">/</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e69c60b553f06d3463460a9f4cee3c01"><span class="id" title="notation">}</span></a>) (<a name="Elim1.f_id"><span class="id" title="variable">f_id</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a>).<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_endo"><span class="id" title="lemma">big_endo</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1.f"><span class="id" title="variable">f</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Elim1"><span class="id" title="section">Elim1</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Extensionality"><span class="id" title="section">Extensionality</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Extensionality.R"><span class="id" title="variable">R</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Extensionality.idx"><span class="id" title="variable">idx</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a>) (<a name="Extensionality.op"><span class="id" title="variable">op</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#R"><span class="id" title="variable">R</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Extensionality.SeqExtension"><span class="id" title="section">SeqExtension</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a> : <span class="id" title="keyword">Type</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="foldrE"><span class="id" title="lemma">foldrE</span></a> <span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#foldr"><span class="id" title="definition">foldr</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_filter"><span class="id" title="lemma">big_filter</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#filter"><span class="id" title="definition">filter</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_filter_cond"><span class="id" title="lemma">big_filter_cond</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P1</span> <span class="id" title="var">P2</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#filter"><span class="id" title="definition">filter</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_bigl"><span class="id" title="lemma">eq_bigl</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P1</span> <span class="id" title="var">P2</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - A lemma to permute aggregate conditions. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="big_andbC"><span class="id" title="lemma">big_andbC</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> <span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_bigr"><span class="id" title="lemma">eq_bigr</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_big"><span class="id" title="lemma">eq_big</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P1</span> <span class="id" title="var">P2</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="congr_big"><span class="id" title="lemma">congr_big</span></a> <span class="id" title="var">r1</span> <span class="id" title="var">r2</span> (<span class="id" title="var">P1</span> <span class="id" title="var">P2</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nil"><span class="id" title="lemma">big_nil</span></a> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#0a934e621391740b862762275992e626"><span class="id" title="notation">[::]</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_cons"><span class="id" title="lemma">big_cons</span></a> <span class="id" title="var">i</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">x</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#407cde5b61fbf27196d1a7c5a475e083"><span class="id" title="notation">::</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_map"><span class="id" title="lemma">big_map</span></a> <span class="id" title="var">J</span> (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nth"><span class="id" title="lemma">big_nth</span></a> <span class="id" title="var">x0</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#nth"><span class="id" title="definition">nth</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#nth"><span class="id" title="definition">nth</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_hasC"><span class="id" title="lemma">big_hasC</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#has"><span class="id" title="definition">has</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_pred0_eq"><span class="id" title="lemma">big_pred0_eq</span></a> (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_pred0"><span class="id" title="lemma">big_pred0</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#xpred0"><span class="id" title="abbreviation">xpred0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_cat_nested"><span class="id" title="lemma">big_cat_nested</span></a> <span class="id" title="var">r1</span> <span class="id" title="var">r2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">x</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#93e0a78b945d3f9f22195c004c67aa36"><span class="id" title="notation">++</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_catl"><span class="id" title="lemma">big_catl</span></a> <span class="id" title="var">r1</span> <span class="id" title="var">r2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#has"><span class="id" title="definition">has</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#93e0a78b945d3f9f22195c004c67aa36"><span class="id" title="notation">++</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_catr"><span class="id" title="lemma">big_catr</span></a> <span class="id" title="var">r1</span> <span class="id" title="var">r2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#has"><span class="id" title="definition">has</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#93e0a78b945d3f9f22195c004c67aa36"><span class="id" title="notation">++</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_const_seq"><span class="id" title="lemma">big_const_seq</span></a> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension.I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#count"><span class="id" title="definition">count</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.SeqExtension"><span class="id" title="section">SeqExtension</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_map_id"><span class="id" title="lemma">big_map_id</span></a> <span class="id" title="var">J</span> (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#map"><span class="id" title="definition">map</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - The following lemmas can be used to localise extensionality to a specific - index sequence. This is done by ssreflect rewriting, before applying - congruence or induction lemmas. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="big_seq_cond"><span class="id" title="lemma">big_seq_cond</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_seq"><span class="id" title="lemma">big_seq</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_big_seq"><span class="id" title="lemma">eq_big_seq</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Similar lemmas for exposing integer indexing in the predicate. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="big_nat_cond"><span class="id" title="lemma">big_nat_cond</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nat"><span class="id" title="lemma">big_nat</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="congr_big_nat"><span class="id" title="lemma">congr_big_nat</span></a> <span class="id" title="var">m1</span> <span class="id" title="var">n1</span> <span class="id" title="var">m2</span> <span class="id" title="var">n2</span> <span class="id" title="var">P1</span> <span class="id" title="var">P2</span> <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m2"><span class="id" title="variable">m2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m2"><span class="id" title="variable">m2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_big_nat"><span class="id" title="lemma">eq_big_nat</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_geq"><span class="id" title="lemma">big_geq</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#73030c22bc0b1fa771c65aa5414c65f9"><span class="id" title="notation">≥</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ltn_cond"><span class="id" title="lemma">big_ltn_cond</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">let</span> <span class="id" title="var">x</span> := <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ltn"><span class="id" title="lemma">big_ltn</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_addn"><span class="id" title="lemma">big_addn</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> <span class="id" title="var">a</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7825ccc99f23b0d30c9d40c317ba7af0"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_add1"><span class="id" title="lemma">big_add1</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#f953bf7095e0da1cb644443fd0e17d6d"><span class="id" title="notation">.-1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nat_recl"><span class="id" title="lemma">big_nat_recl</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_mkord"><span class="id" title="lemma">big_mkord</span></a> <span class="id" title="var">n</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a>0 <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nat_widen"><span class="id" title="lemma">big_nat_widen</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_widen_cond"><span class="id" title="lemma">big_ord_widen_cond</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_widen"><span class="id" title="lemma">big_ord_widen</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> (<span class="id" title="var">F</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_widen_leq"><span class="id" title="lemma">big_ord_widen_leq</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">)</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#inord"><span class="id" title="definition">inord</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#inord"><span class="id" title="definition">inord</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord0"><span class="id" title="lemma">big_ord0</span></a> <span class="id" title="var">P</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> 0 <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_tnth"><span class="id" title="lemma">big_tnth</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">r_</span> := <a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> (<a class="idref" href="mathcomp.ssreflect.tuple.html#in_tuple"><span class="id" title="definition">in_tuple</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a>) <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#r_"><span class="id" title="variable">r_</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#r_"><span class="id" title="variable">r_</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_index_uniq"><span class="id" title="lemma">big_index_uniq</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">E</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#oapp"><span class="id" title="abbreviation">oapp</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a> (<a class="idref" href="mathcomp.ssreflect.eqtype.html#insub"><span class="id" title="definition">insub</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#index"><span class="id" title="definition">index</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a>)).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_tuple"><span class="id" title="lemma">big_tuple</span></a> <span class="id" title="var">I</span> <span class="id" title="var">n</span> (<span class="id" title="var">t</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#c3913abe839346eb60d82da74b0b1f67"><span class="id" title="notation">.-</span></a><a class="idref" href="mathcomp.ssreflect.tuple.html#c3913abe839346eb60d82da74b0b1f67"><span class="id" title="notation">tuple</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#t"><span class="id" title="variable">t</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#t"><span class="id" title="variable">t</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.tuple.html#tnth"><span class="id" title="definition">tnth</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#t"><span class="id" title="variable">t</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_narrow_cond"><span class="id" title="lemma">big_ord_narrow_cond</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">I_n2</span></a>) <span class="id" title="var">F</span> (<span class="id" title="var">le_n12</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a>) :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">w</span> := <a class="idref" href="mathcomp.ssreflect.fintype.html#widen_ord"><span class="id" title="definition">widen_ord</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#le_n12"><span class="id" title="variable">le_n12</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#w"><span class="id" title="variable">w</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#w"><span class="id" title="variable">w</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_narrow_cond_leq"><span class="id" title="lemma">big_ord_narrow_cond_leq</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <span class="id" title="var">_</span>) <span class="id" title="var">F</span> (<span class="id" title="var">le_n12</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a>) :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">w</span> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#widen_ord"><span class="id" title="definition">widen_ord</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#le_n12"><span class="id" title="variable">le_n12</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#w"><span class="id" title="variable">w</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#w"><span class="id" title="variable">w</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_narrow"><span class="id" title="lemma">big_ord_narrow</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> <span class="id" title="var">F</span> (<span class="id" title="var">le_n12</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a>) :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">w</span> := <a class="idref" href="mathcomp.ssreflect.fintype.html#widen_ord"><span class="id" title="definition">widen_ord</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#le_n12"><span class="id" title="variable">le_n12</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#w"><span class="id" title="variable">w</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_narrow_leq"><span class="id" title="lemma">big_ord_narrow_leq</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> <span class="id" title="var">F</span> (<span class="id" title="var">le_n12</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a>) :<br/> - <span class="id" title="keyword">let</span> <span class="id" title="var">w</span> := @<a class="idref" href="mathcomp.ssreflect.fintype.html#widen_ord"><span class="id" title="definition">widen_ord</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#le_n12"><span class="id" title="variable">le_n12</span></a> <span class="id" title="tactic">in</span><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#w"><span class="id" title="variable">w</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_recl"><span class="id" title="lemma">big_ord_recl</span></a> <span class="id" title="var">n</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ord0"><span class="id" title="definition">ord0</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (@<a class="idref" href="mathcomp.ssreflect.fintype.html#lift"><span class="id" title="definition">lift</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ord0"><span class="id" title="definition">ord0</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_const"><span class="id" title="lemma">big_const</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_const_nat"><span class="id" title="lemma">big_const_nat</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7825ccc99f23b0d30c9d40c317ba7af0"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_const_ord"><span class="id" title="lemma">big_const_ord</span></a> <span class="id" title="var">n</span> <span class="id" title="var">x</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nseq_cond"><span class="id" title="lemma">big_nseq_cond</span></a> <span class="id" title="var">I</span> <span class="id" title="var">n</span> <span class="id" title="var">a</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#nseq"><span class="id" title="definition">nseq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a>)) <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nseq"><span class="id" title="lemma">big_nseq</span></a> <span class="id" title="var">I</span> <span class="id" title="var">n</span> <span class="id" title="var">a</span> (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>):<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#nseq"><span class="id" title="definition">nseq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iter"><span class="id" title="definition">iter</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a>)) <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_image_cond"><span class="id" title="lemma">big_image_cond</span></a> <span class="id" title="var">I</span> (<span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_image"><span class="id" title="lemma">big_image</span></a> <span class="id" title="var">I</span> (<span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_image_cond_id"><span class="id" title="lemma">big_image_cond_id</span></a> (<span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_image_id"><span class="id" title="lemma">big_image_id</span></a> (<span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.R"><span class="id" title="variable">R</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">|</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c3ff8d84d4e3e273bebfcf7502deb41a"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Extensionality"><span class="id" title="section">Extensionality</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="MonoidProperties"><span class="id" title="section">MonoidProperties</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Monoid.Theory</span>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="MonoidProperties.R"><span class="id" title="variable">R</span></a> : <span class="id" title="keyword">Type</span>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="MonoidProperties.idx"><span class="id" title="variable">idx</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties.R"><span class="id" title="variable">R</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="MonoidProperties.Plain"><span class="id" title="section">Plain</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="MonoidProperties.Plain.op"><span class="id" title="variable">op</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#law"><span class="id" title="record">Monoid.law</span></a> 1.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="foldlE"><span class="id" title="lemma">foldlE</span></a> <span class="id" title="var">x</span> <span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#foldl"><span class="id" title="definition">foldl</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#407cde5b61fbf27196d1a7c5a475e083"><span class="id" title="notation">::</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="foldl_idx"><span class="id" title="lemma">foldl_idx</span></a> <span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#foldl"><span class="id" title="definition">foldl</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a> 1 <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_big_idx_seq"><span class="id" title="lemma">eq_big_idx_seq</span></a> <span class="id" title="var">idx'</span> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_id"><span class="id" title="definition">right_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#idx'"><span class="id" title="variable">idx'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#has"><span class="id" title="definition">has</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#idx'"><span class="id" title="variable">idx'</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_big_idx"><span class="id" title="lemma">eq_big_idx</span></a> <span class="id" title="var">idx'</span> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">i0</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#right_id"><span class="id" title="definition">right_id</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#idx'"><span class="id" title="variable">idx'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#idx'"><span class="id" title="variable">idx'</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big1_eq"><span class="id" title="lemma">big1_eq</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) : <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big1"><span class="id" title="lemma">big1</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big1_seq"><span class="id" title="lemma">big1_seq</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_seq1"><span class="id" title="lemma">big_seq1</span></a> <span class="id" title="var">I</span> (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_mkcond"><span class="id" title="lemma">big_mkcond</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> 1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_mkcondr"><span class="id" title="lemma">big_mkcondr</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> <span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> 1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_mkcondl"><span class="id" title="lemma">big_mkcondl</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> <span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> 1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_cat"><span class="id" title="lemma">big_cat</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r1</span> <span class="id" title="var">r2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#93e0a78b945d3f9f22195c004c67aa36"><span class="id" title="notation">++</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_allpairs_dep"><span class="id" title="lemma">big_allpairs_dep</span></a> <span class="id" title="var">I1</span> (<span class="id" title="var">I2</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I1"><span class="id" title="variable">I1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <span class="id" title="keyword">Type</span>) <span class="id" title="var">J</span> (<span class="id" title="var">h</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i1</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#I2"><span class="id" title="variable">I2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>)<br/> - (<span class="id" title="var">r1</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I1"><span class="id" title="variable">I1</span></a>) (<span class="id" title="var">r2</span> : <span class="id" title="keyword">∀</span> <span class="id" title="var">i1</span>, <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#I2"><span class="id" title="variable">I2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a>)) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i2"><span class="id" title="variable">i2</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">|</span></a> <span class="id" title="var">i1</span> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">,</span></a> <span class="id" title="var">i2</span> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i1</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i2</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i2"><span class="id" title="variable">i2</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_allpairs"><span class="id" title="lemma">big_allpairs</span></a> <span class="id" title="var">I1</span> <span class="id" title="var">I2</span> (<span class="id" title="var">r1</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I1"><span class="id" title="variable">I1</span></a>) (<span class="id" title="var">r2</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I2"><span class="id" title="variable">I2</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">seq</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i2"><span class="id" title="variable">i2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">|</span></a> <span class="id" title="var">i1</span> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">,</span></a> <span class="id" title="var">i2</span> <a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#623af7e6d063f6c25f88725170ed3a4c"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i1</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties.Plain.op"><span class="id" title="variable">op</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties.idx"><span class="id" title="variable">idx</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i2</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i1"><span class="id" title="variable">i1</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i2"><span class="id" title="variable">i2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_pred1_eq"><span class="id" title="lemma">big_pred1_eq</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">i</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_pred1"><span class="id" title="lemma">big_pred1</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">i</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#pred1"><span class="id" title="definition">pred1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_cat_nat"><span class="id" title="lemma">big_cat_nat</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span> <span class="id" title="var">p</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nat1"><span class="id" title="lemma">big_nat1</span></a> <span class="id" title="var">n</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nat_recr"><span class="id" title="lemma">big_nat_recr</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_ord_recr"><span class="id" title="lemma">big_ord_recr</span></a> <span class="id" title="var">n</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#widen_ord"><span class="id" title="definition">widen_ord</span></a> (<a class="idref" href="mathcomp.ssreflect.ssrnat.html#leqnSn"><span class="id" title="lemma">leqnSn</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ord_max"><span class="id" title="definition">ord_max</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_sumType"><span class="id" title="lemma">big_sumType</span></a> (<span class="id" title="var">I1</span> <span class="id" title="var">I2</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#I1"><span class="id" title="variable">I1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#e03f39daf98516fa530d3f6f5a1b4d92"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I2"><span class="id" title="variable">I2</span></a>)) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#inl"><span class="id" title="constructor">inl</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#inl"><span class="id" title="constructor">inl</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#inr"><span class="id" title="constructor">inr</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#inr"><span class="id" title="constructor">inr</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_split_ord"><span class="id" title="lemma">big_split_ord</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">'</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">I_</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#545d9d6249a673300f950a2a8b8a930b"><span class="id" title="notation">)</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#lshift"><span class="id" title="definition">lshift</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#lshift"><span class="id" title="definition">lshift</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#rshift"><span class="id" title="definition">rshift</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#rshift"><span class="id" title="definition">rshift</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d3310823c977c18402e087052356682e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_flatten"><span class="id" title="lemma">big_flatten</span></a> <span class="id" title="var">I</span> <span class="id" title="var">rr</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#flatten"><span class="id" title="definition">flatten</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rr"><span class="id" title="variable">rr</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">r</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rr"><span class="id" title="variable">rr</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fc6b31eb5a9c190f3c69acfe152eb8da"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties.Plain"><span class="id" title="section">Plain</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="MonoidProperties.Abelian"><span class="id" title="section">Abelian</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="MonoidProperties.Abelian.op"><span class="id" title="variable">op</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#com_law"><span class="id" title="record">Monoid.com_law</span></a> 1.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="perm_big"><span class="id" title="lemma">perm_big</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) <span class="id" title="var">r1</span> <span class="id" title="var">r2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.seq.html#perm_eq"><span class="id" title="definition">perm_eq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_uniq"><span class="id" title="lemma">big_uniq</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_rem"><span class="id" title="lemma">big_rem</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) <span class="id" title="var">r</span> <span class="id" title="var">x</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">(</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">if</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">then</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#00a1a5b58aac8f1e3f1abff064a39f9d"><span class="id" title="notation">else</span></a> 1<a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#rem"><span class="id" title="definition">rem</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#y"><span class="id" title="variable">y</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_undup"><span class="id" title="lemma">big_undup</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#idempotent"><span class="id" title="definition">idempotent</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#undup"><span class="id" title="definition">undup</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_big_idem"><span class="id" title="lemma">eq_big_idem</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">r1</span> <span class="id" title="var">r2</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#idempotent"><span class="id" title="definition">idempotent</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">=</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#1e6a438ff685c38fcd9034a94f271777"><span class="id" title="notation">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r1"><span class="id" title="variable">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r2"><span class="id" title="variable">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_undup_iterop_count"><span class="id" title="lemma">big_undup_iterop_count</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#undup"><span class="id" title="definition">undup</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#iterop"><span class="id" title="definition">iterop</span></a> (<a class="idref" href="mathcomp.ssreflect.seq.html#count_mem"><span class="id" title="abbreviation">count_mem</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) 1<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_split"><span class="id" title="lemma">big_split</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F1</span> <span class="id" title="var">F2</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F1"><span class="id" title="variable">F1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F2"><span class="id" title="variable">F2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigID"><span class="id" title="lemma">bigID</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">a</span> <span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">×</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">~~</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigU"><span class="id" title="lemma">bigU</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">disjoint</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5eb5169ac355423e8c7c929c40b7aef7"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5eb5169ac355423e8c7c929c40b7aef7"><span class="id" title="notation">predU</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5eb5169ac355423e8c7c929c40b7aef7"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5eb5169ac355423e8c7c929c40b7aef7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigD1"><span class="id" title="lemma">bigD1</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">j</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigD1_seq"><span class="id" title="lemma">bigD1_seq</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">j</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#uniq"><span class="id" title="definition">uniq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#fa96cf288c7d631ec59b7d16f33878eb"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardD1x"><span class="id" title="lemma">cardD1x</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">j</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#SimplPred"><span class="id" title="definition">SimplPred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#08a7ed80cdc6170ce1653a381b05d13e"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#08a7ed80cdc6170ce1653a381b05d13e"><span class="id" title="notation">pred</span></a> <span class="id" title="var">i</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#08a7ed80cdc6170ce1653a381b05d13e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#08a7ed80cdc6170ce1653a381b05d13e"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#08a7ed80cdc6170ce1653a381b05d13e"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="partition_big"><span class="id" title="lemma">partition_big</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">p</span> (<span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="reindex_onto"><span class="id" title="lemma">reindex_onto</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">h'</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h'"><span class="id" title="variable">h'</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>) <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#h'"><span class="id" title="variable">h'</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>) <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="reindex"><span class="id" title="lemma">reindex</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#7a12faf7e5f15d58335f3e4b34342ab7"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#7a12faf7e5f15d58335f3e4b34342ab7"><span class="id" title="notation">on</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">pred</span></a> <span class="id" title="var">i</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#7a12faf7e5f15d58335f3e4b34342ab7"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#7a12faf7e5f15d58335f3e4b34342ab7"><span class="id" title="notation">bijective</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#7a12faf7e5f15d58335f3e4b34342ab7"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="reindex_inj"><span class="id" title="lemma">reindex_inj</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#injective"><span class="id" title="definition">injective</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_nat_rev"><span class="id" title="lemma">big_nat_rev</span></a> <span class="id" title="var">m</span> <span class="id" title="var">n</span> <span class="id" title="var">P</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7825ccc99f23b0d30c9d40c317ba7af0"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">+</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7825ccc99f23b0d30c9d40c317ba7af0"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">.+1</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pair_big_dep"><span class="id" title="lemma">pair_big_dep</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><span class="id" title="notation">.2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><span class="id" title="notation">.2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pair_big"><span class="id" title="lemma">pair_big</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">p</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><span class="id" title="notation">.2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><span class="id" title="notation">.2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pair_bigA"><span class="id" title="lemma">pair_bigA</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_j</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_p</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#e0817251e7d67ad994b4d9b1aa82a412"><span class="id" title="notation">.1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#p"><span class="id" title="variable">p</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#675082cc4d4538da052b547bdc6ea4c9"><span class="id" title="notation">.2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="exchange_big_dep"><span class="id" title="lemma">exchange_big_dep</span></a> <span class="id" title="var">I</span> <span class="id" title="var">J</span> <span class="id" title="var">rI</span> <span class="id" title="var">rJ</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>)<br/> - (<span class="id" title="var">xQ</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span> <span class="id" title="var">j</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#xQ"><span class="id" title="variable">xQ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rI"><span class="id" title="variable">rI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rJ"><span class="id" title="variable">rJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rJ"><span class="id" title="variable">rJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#xQ"><span class="id" title="variable">xQ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rI"><span class="id" title="variable">rI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="exchange_big"><span class="id" title="lemma">exchange_big</span></a> <span class="id" title="var">I</span> <span class="id" title="var">J</span> <span class="id" title="var">rI</span> <span class="id" title="var">rJ</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rI"><span class="id" title="variable">rI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rJ"><span class="id" title="variable">rJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rJ"><span class="id" title="variable">rJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rI"><span class="id" title="variable">rI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="exchange_big_dep_nat"><span class="id" title="lemma">exchange_big_dep_nat</span></a> <span class="id" title="var">m1</span> <span class="id" title="var">n1</span> <span class="id" title="var">m2</span> <span class="id" title="var">n2</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>)<br/> - (<span class="id" title="var">xQ</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span> <span class="id" title="var">j</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m2"><span class="id" title="variable">m2</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea090076ab3dcdee0cfd3882c88b993f"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#xQ"><span class="id" title="variable">xQ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m2"><span class="id" title="variable">m2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m2"><span class="id" title="variable">m2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#xQ"><span class="id" title="variable">xQ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="exchange_big_nat"><span class="id" title="lemma">exchange_big_nat</span></a> <span class="id" title="var">m1</span> <span class="id" title="var">n1</span> <span class="id" title="var">m2</span> <span class="id" title="var">n2</span> (<span class="id" title="var">P</span> <span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m2"><span class="id" title="variable">m2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m2"><span class="id" title="variable">m2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#4461abbe51a521b546e6aa0e9d87a0f5"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#m1"><span class="id" title="variable">m1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties.Abelian"><span class="id" title="section">Abelian</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#MonoidProperties"><span class="id" title="section">MonoidProperties</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Distributivity"><span class="id" title="section">Distributivity</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Import</span> <span class="id" title="var">Monoid.Theory</span>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="Distributivity.R"><span class="id" title="variable">R</span></a> : <span class="id" title="keyword">Type</span>.<br/> -<span class="id" title="keyword">Variables</span> <a name="Distributivity.zero"><span class="id" title="variable">zero</span></a> <a name="Distributivity.one"><span class="id" title="variable">one</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Distributivity.R"><span class="id" title="variable">R</span></a>.<br/> -<span class="id" title="keyword">Variable</span> <a name="Distributivity.times"><span class="id" title="variable">times</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#mul_law"><span class="id" title="record">Monoid.mul_law</span></a> 0.<br/> -<span class="id" title="keyword">Variable</span> <a name="Distributivity.plus"><span class="id" title="variable">plus</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#add_law"><span class="id" title="record">Monoid.add_law</span></a> 0 <a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_distrl"><span class="id" title="lemma">big_distrl</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> <span class="id" title="var">a</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_distrr"><span class="id" title="lemma">big_distrr</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> <span class="id" title="var">a</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_distrlr"><span class="id" title="lemma">big_distrlr</span></a> <span class="id" title="var">I</span> <span class="id" title="var">J</span> <span class="id" title="var">rI</span> <span class="id" title="var">rJ</span> (<span class="id" title="var">pI</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">pJ</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> <span class="id" title="var">G</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rI"><span class="id" title="variable">rI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#pI"><span class="id" title="variable">pI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rJ"><span class="id" title="variable">rJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#pJ"><span class="id" title="variable">pJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">)</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rI"><span class="id" title="variable">rI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#pI"><span class="id" title="variable">pI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#rJ"><span class="id" title="variable">rJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#pJ"><span class="id" title="variable">pJ</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#909fafebcac054e6ea1f51c42cc5d7e4"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_distr_big_dep"><span class="id" title="lemma">big_distr_big_dep</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">j0</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">f</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finfun.html#pfamily"><span class="id" title="abbreviation">pfamily</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j0"><span class="id" title="variable">j0</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_distr_big"><span class="id" title="lemma">big_distr_big</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">j0</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">f</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finfun.html#pffun_on"><span class="id" title="abbreviation">pffun_on</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j0"><span class="id" title="variable">j0</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigA_distr_big_dep"><span class="id" title="lemma">bigA_distr_big_dep</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">f</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finfun.html#family"><span class="id" title="abbreviation">family</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigA_distr_big"><span class="id" title="lemma">bigA_distr_big</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">Q</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Distributivity.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">(</span></a><span class="id" title="var">f</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finfun.html#ffun_on"><span class="id" title="abbreviation">ffun_on</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#Q"><span class="id" title="variable">Q</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigA_distr_bigA"><span class="id" title="lemma">bigA_distr_bigA</span></a> (<span class="id" title="var">I</span> <span class="id" title="var">J</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">+%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#88fba592ed3d4e098c5d35d419ba227d"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">(</span></a><span class="id" title="var">f</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finfun.html#31493a873acc18a8368490ef56022c0c"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#31493a873acc18a8368490ef56022c0c"><span class="id" title="notation">ffun</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#31493a873acc18a8368490ef56022c0c"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">*%</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#e4a543eb2341808c894b69ea952364a0"><span class="id" title="notation">M</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">/</span></a>1<a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#379a79a86133b2d1cd9cb43efa183ecb"><span class="id" title="notation">_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> (<a class="idref" href="mathcomp.ssreflect.bigop.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#Distributivity"><span class="id" title="section">Distributivity</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="BigBool"><span class="id" title="section">BigBool</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="BigBool.Seq"><span class="id" title="section">Seq</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="BigBool.Seq.I"><span class="id" title="variable">I</span></a> : <span class="id" title="keyword">Type</span>) (<a name="BigBool.Seq.r"><span class="id" title="variable">r</span></a> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<a name="BigBool.Seq.P"><span class="id" title="variable">P</span></a> <a name="BigBool.Seq.B"><span class="id" title="variable">B</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_has"><span class="id" title="lemma">big_has</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#orb"><span class="id" title="definition">orb</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#has"><span class="id" title="definition">has</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_all"><span class="id" title="lemma">big_all</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#andb"><span class="id" title="definition">andb</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#all"><span class="id" title="definition">all</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_has_cond"><span class="id" title="lemma">big_has_cond</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#orb"><span class="id" title="definition">orb</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#has"><span class="id" title="definition">has</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#predI"><span class="id" title="definition">predI</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a>) <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_all_cond"><span class="id" title="lemma">big_all_cond</span></a> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#andb"><span class="id" title="definition">andb</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">/</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#60e57ff387b8a0840e944d0d03f215e2"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#all"><span class="id" title="definition">all</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">pred</span></a> <span class="id" title="var">i</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#a133e82bab56729f895f9b2b31e837cd"><span class="id" title="notation">==></span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq.r"><span class="id" title="variable">r</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.Seq"><span class="id" title="section">Seq</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="BigBool.FinType"><span class="id" title="section">FinType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="BigBool.FinType.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="BigBool.FinType.P"><span class="id" title="variable">P</span></a> <a name="BigBool.FinType.B"><span class="id" title="variable">B</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_orE"><span class="id" title="lemma">big_orE</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#orb"><span class="id" title="definition">orb</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#e9122b3568d6f47f958b76a6e55e4e40"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#e9122b3568d6f47f958b76a6e55e4e40"><span class="id" title="notation">∃</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#e9122b3568d6f47f958b76a6e55e4e40"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#e9122b3568d6f47f958b76a6e55e4e40"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#e9122b3568d6f47f958b76a6e55e4e40"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#e9122b3568d6f47f958b76a6e55e4e40"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_andE"><span class="id" title="lemma">big_andE</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#andb"><span class="id" title="definition">andb</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#true"><span class="id" title="constructor">true</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">∀</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType.B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool.FinType"><span class="id" title="section">FinType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#BigBool"><span class="id" title="section">BigBool</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="NatConst"><span class="id" title="section">NatConst</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="NatConst.I"><span class="id" title="variable">I</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="NatConst.A"><span class="id" title="variable">A</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sum_nat_const"><span class="id" title="lemma">sum_nat_const</span></a> <span class="id" title="var">n</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#NatConst.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#NatConst.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sum1_card"><span class="id" title="lemma">sum1_card</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#NatConst.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">)</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#NatConst.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sum1_count"><span class="id" title="lemma">sum1_count</span></a> <span class="id" title="var">J</span> (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) (<span class="id" title="var">a</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) : <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">)</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#count"><span class="id" title="definition">count</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sum1_size"><span class="id" title="lemma">sum1_size</span></a> <span class="id" title="var">J</span> (<span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#seq"><span class="id" title="abbreviation">seq</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#J"><span class="id" title="variable">J</span></a>) : <a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">)</span></a> 1 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#size"><span class="id" title="definition">size</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="prod_nat_const"><span class="id" title="lemma">prod_nat_const</span></a> <span class="id" title="var">n</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#2e5c92af4bc9a12f0e6a46802637177b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#2e5c92af4bc9a12f0e6a46802637177b"><span class="id" title="notation">prod_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#2e5c92af4bc9a12f0e6a46802637177b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#2e5c92af4bc9a12f0e6a46802637177b"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#NatConst.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#2e5c92af4bc9a12f0e6a46802637177b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#NatConst.A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sum_nat_const_nat"><span class="id" title="lemma">sum_nat_const_nat</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> <span class="id" title="var">n</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#c0980ea1654f471922ad26f5837d48da"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#c0980ea1654f471922ad26f5837d48da"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#c0980ea1654f471922ad26f5837d48da"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#c0980ea1654f471922ad26f5837d48da"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#c0980ea1654f471922ad26f5837d48da"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#c0980ea1654f471922ad26f5837d48da"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7825ccc99f23b0d30c9d40c317ba7af0"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="prod_nat_const_nat"><span class="id" title="lemma">prod_nat_const_nat</span></a> <span class="id" title="var">n1</span> <span class="id" title="var">n2</span> <span class="id" title="var">n</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#b46f4e825b398c0eb860f658bff447f6"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#b46f4e825b398c0eb860f658bff447f6"><span class="id" title="notation">prod_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#b46f4e825b398c0eb860f658bff447f6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#b46f4e825b398c0eb860f658bff447f6"><span class="id" title="notation">≤</span></a> <span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#b46f4e825b398c0eb860f658bff447f6"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#b46f4e825b398c0eb860f658bff447f6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n"><span class="id" title="variable">n</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#n2"><span class="id" title="variable">n2</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7825ccc99f23b0d30c9d40c317ba7af0"><span class="id" title="notation">-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#n1"><span class="id" title="variable">n1</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#NatConst"><span class="id" title="section">NatConst</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sumnE"><span class="id" title="lemma">sumnE</span></a> <span class="id" title="var">r</span> : <a class="idref" href="mathcomp.ssreflect.seq.html#sumn"><span class="id" title="definition">sumn</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#3c5ded5149162c47f03c637c983c78c4"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>. <br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="leqif_sum"><span class="id" title="lemma">leqif_sum</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> <span class="id" title="var">C</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">E1</span> <span class="id" title="var">E2</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E1"><span class="id" title="variable">E1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E2"><span class="id" title="variable">E2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">?=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">iff</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E1"><span class="id" title="variable">E1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E2"><span class="id" title="variable">E2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">?=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">iff</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">∀</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="leq_sum"><span class="id" title="lemma">leq_sum</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">E1</span> <span class="id" title="var">E2</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E1"><span class="id" title="variable">E1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E2"><span class="id" title="variable">E2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E1"><span class="id" title="variable">E1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E2"><span class="id" title="variable">E2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sum_nat_eq0"><span class="id" title="lemma">sum_nat_eq0</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">E</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) :<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 0)%<span class="id" title="var">N</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">∀</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 0%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.fintype.html#90a753c4c9a43b6ba4178e7bc1e47801"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="prodn_cond_gt0"><span class="id" title="lemma">prodn_cond_gt0</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> 0 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> 0 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">prod_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="prodn_gt0"><span class="id" title="lemma">prodn_gt0</span></a> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, 0 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> 0 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><span class="id" title="notation"><</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">prod_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="leq_bigmax_cond"><span class="id" title="lemma">leq_bigmax_cond</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> <span class="id" title="var">i0</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">max_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="leq_bigmax"><span class="id" title="lemma">leq_bigmax</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">F</span> (<span class="id" title="var">i0</span> : <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) : <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d7221eb7e755bf25abb3156848a10d4b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d7221eb7e755bf25abb3156848a10d4b"><span class="id" title="notation">max_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigmax_leqP"><span class="id" title="lemma">bigmax_leqP</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">m</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">max_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigmax_sup"><span class="id" title="lemma">bigmax_sup</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">i0</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">m</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">max_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigmax_eq_arg"><span class="id" title="lemma">bigmax_eq_arg</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">i0</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">max_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#168cda9d261f63f91aed3ac3e417d194"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">arg</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">max_</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">></span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#93615dc0fa359e70f6f3e6106709d1fb"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_bigmax_cond"><span class="id" title="lemma">eq_bigmax_cond</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7f2a7ef2c63af7359b22787a9daf336e"><span class="id" title="notation">></span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">{</span></a><span class="id" title="var">i0</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#ec60518d5ab0e853ea27ade01a2f345b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#ec60518d5ab0e853ea27ade01a2f345b"><span class="id" title="notation">max_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#ec60518d5ab0e853ea27ade01a2f345b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#ec60518d5ab0e853ea27ade01a2f345b"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#ec60518d5ab0e853ea27ade01a2f345b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_bigmax"><span class="id" title="lemma">eq_bigmax</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#7f2a7ef2c63af7359b22787a9daf336e"><span class="id" title="notation">></span></a> 0 <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">{</span></a><span class="id" title="var">i0</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d7221eb7e755bf25abb3156848a10d4b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d7221eb7e755bf25abb3156848a10d4b"><span class="id" title="notation">max_i</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#6556914db359db999889decec6a4a562"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="expn_sum"><span class="id" title="lemma">expn_sum</span></a> <span class="id" title="var">m</span> <span class="id" title="var">I</span> <span class="id" title="var">r</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> :<br/> - (<a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">sum_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f9660601caed2f1f92279ff134c53c8a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">prod_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#f442bb2e94ef4d788c146d8499003144"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#81fd94e251a61ee523cdd7855774ae7c"><span class="id" title="notation">^</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>)%<span class="id" title="var">N</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="dvdn_biglcmP"><span class="id" title="lemma">dvdn_biglcmP</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> <span class="id" title="var">m</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.div.html#lcmn"><span class="id" title="definition">lcmn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="biglcmn_sup"><span class="id" title="lemma">biglcmn_sup</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">i0</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> <span class="id" title="var">m</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.div.html#lcmn"><span class="id" title="definition">lcmn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>1%<span class="id" title="var">N</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="dvdn_biggcdP"><span class="id" title="lemma">dvdn_biggcdP</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> <span class="id" title="var">m</span> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#reflect"><span class="id" title="abbreviation">reflect</span></a> (<span class="id" title="keyword">∀</span> <span class="id" title="var">i</span>, <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.div.html#gcdn"><span class="id" title="definition">gcdn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="biggcdn_inf"><span class="id" title="lemma">biggcdn_inf</span></a> (<span class="id" title="var">I</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) <span class="id" title="var">i0</span> (<span class="id" title="var">P</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#pred"><span class="id" title="definition">pred</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#I"><span class="id" title="variable">I</span></a>) <span class="id" title="var">F</span> <span class="id" title="var">m</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i0"><span class="id" title="variable">i0</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">big</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.div.html#gcdn"><span class="id" title="definition">gcdn</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a>0<a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">_</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.div.html#bde82eab2fe4a0799bc2419e587505d4"><span class="id" title="notation">%|</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#m"><span class="id" title="variable">m</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">"</span></a>@ 'eq_big_perm'" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.ssreflect.html#Deprecation.Exports.deprecate"><span class="id" title="abbreviation">deprecate</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#eq_big_perm"><span class="id" title="variable">eq_big_perm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#perm_big"><span class="id" title="variable">perm_big</span></a>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 10, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="eq_big_perm"><span class="id" title="abbreviation">eq_big_perm</span></a> :=<br/> - ((<span class="id" title="keyword">fun</span> <span class="id" title="var">R</span> <span class="id" title="var">idx</span> <span class="id" title="var">op</span> <span class="id" title="var">I</span> <span class="id" title="var">r1</span> <span class="id" title="var">P</span> <span class="id" title="var">F</span> <span class="id" title="var">r2</span> ⇒ <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">@</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">eq_big_perm</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">R</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">idx</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">op</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">I</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">r1</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">r2</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#866c6556476c4a4b6eba6ff567c37fde"><span class="id" title="notation">F</span></a>)<br/> - <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span> <span class="id" title="var">_</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> -</div> -</div> - -<div id="footer"> -<hr/><a href="index.html">Index</a><hr/>This page has been generated by <a href="http://coq.inria.fr/">coqdoc</a> -</div> - -</div> - -</body> -</html>
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