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diff --git a/docs/htmldoc/mathcomp.ssreflect.finset.html b/docs/htmldoc/mathcomp.ssreflect.finset.html deleted file mode 100644 index b9f69c8..0000000 --- a/docs/htmldoc/mathcomp.ssreflect.finset.html +++ /dev/null @@ -1,2044 +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.finset</title> -</head> - -<body> - -<div id="page"> - -<div id="header"> -</div> - -<div id="main"> - -<h1 class="libtitle">Library mathcomp.ssreflect.finset</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 defines a type for sets over a finite Type, similar to the type - of functions over a finite Type defined in finfun.v (indeed, based in it): - {set T} where T must have a finType structure - We equip {set T} itself with a finType structure, hence Leibnitz and - extensional equalities coincide on {set T}, and we can form {set {set T}} - If A, B : {set T} and P : {set {set T}}, we define: - x \in A == x belongs to A (i.e., {set T} implements predType, - by coercion to pred_sort). - mem A == the predicate corresponding to A. - finset p == the set corresponding to a predicate p. - [set x | P] == the set containing the x such that P is true (x may - appear in P). - [set x | P & Q] := [set x | P && Q]. - [set x in A] == the set containing the x in a collective predicate A. - [set x in A | P] == the set containing the x in A such that P is true. - [set x in A | P & Q] := [set x in A | P && Q]. - All these have typed variants [set x : T | P], [set x : T in A], etc. - set0 == the empty set. - [set: T] or setT == the full set (the A containing all x : T). - A :|: B == the union of A and B. - x |: A == A with the element x added (:= [set x] :| A). - A :&: B == the intersection of A and B. - ~: A == the complement of A. - A :\: B == the difference A minus B. - A :\ x == A with the element x removed (:= A :\: [set x]). - \bigcup<range> A == the union of all A, for i in <range> (i is bound in - A, see bigop.v). - \bigcap<range> A == the intersection of all A, for i in <range>. - cover P == the union of the set of sets P. - trivIset P <=> the elements of P are pairwise disjoint. - partition P A <=> P is a partition of A. - pblock P x == a block of P containing x, or else set0. - equivalence_partition R D == the partition induced on D by the relation R - (provided R is an equivalence relation in D). - preim_partition f D == the partition induced on D by the equivalence - [rel x y | f x == f y]. - is_transversal X P D <=> X is a transversal of the partition P of D. - transversal P D == a transversal of P, provided P is a partition of D. - transversal_repr x0 X B == a representative of B \in P selected by the - tranversal X of P, or else x0. - powerset A == the set of all subset of the set A. - P ::&: A == those sets in P that are subsets of the set A. - f @^-1: A == the preimage of the collective predicate A under f. - f @: A == the image set of the collective predicate A by f. - f @2:(A, B) == the image set of A x B by the binary function f. - [set E | x in A] == the set of all the values of the expression E, for x - drawn from the collective predicate A. - [set E | x in A & P] == the set of values of E for x drawn from A, such - that P is true. - [set E | x in A, y in B] == the set of values of E for x drawn from A and - and y drawn from B; B may depend on x. - [set E | x <- A, y <- B & P] == the set of values of E for x drawn from A - y drawn from B, such that P is trye. - [set E | x : T] == the set of all values of E, with x in type T. - [set E | x : T & P] == the set of values of E for x : T s.t. P is true. - [set E | x : T, y : U in B], [set E | x : T, y : U in B & P], - [set E | x : T in A, y : U], [set E | x : T in A, y : U & P], - [set E | x : T, y : U], [set E | x : T, y : U & P] - == type-ranging versions of the binary comprehensions. - [set E | x : T in A], [set E | x in A, y], [set E | x, y & P], etc. - == typed and untyped variants of the comprehensions above. - The types may be required as type inference processes E - before considering A or B. Note that type casts in the - binary comprehension must either be both present or absent - and that there are no untyped variants for single-type - comprehension as Coq parsing confuses [x | P] and [E | x]. - minset p A == A is a minimal set satisfying p. - maxset p A == A is a maximal set satisfying p. - We also provide notations A :=: B, A :<>: B, A :==: B, A :!=: B, A :=P: B - that specialize A = B, A <> B, A == B, etc., to {set _}. This is useful - for subtypes of {set T}, such as {group T}, that coerce to {set T}. - We give many lemmas on these operations, on card, and on set inclusion. - In addition to the standard suffixes described in ssrbool.v, we associate - the following suffixes to set operations: - 0 -- the empty set, as in in_set0 : (x \in set0) = false. - T -- the full set, as in in_setT : x \in [set: T]. - 1 -- a singleton set, as in in_set1 : (x \in [set a]) = (x == a). - 2 -- an unordered pair, as in - in_set2 : (x \in [set a; b]) = (x == a) || (x == b). - C -- complement, as in setCK : ~: ~: A = A. - I -- intersection, as in setIid : A :&: A = A. - U -- union, as in setUid : A :|: A = A. - D -- difference, as in setDv : A :\: A = set0. - S -- a subset argument, as in - setIS: B \subset C -> A :&: B \subset A :&: C - These suffixes are sometimes preceded with an `s' to distinguish them from - their basic ssrbool interpretation, e.g., - card1 : #|pred1 x| = 1 and cards1 : #| [set x]| = 1 - We also use a trailling `r' to distinguish a right-hand complement from - commutativity, e.g., - setIC : A :&: B = B :&: A and setICr : A :&: ~: A = set0. -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Set Implicit Arguments</span>.<br/> -<span class="id" title="keyword">Section</span> <a name="SetType"><span class="id" title="section">SetType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="SetType.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Inductive</span> <a name="set_type"><span class="id" title="inductive">set_type</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#predArgType"><span class="id" title="definition">predArgType</span></a> := <a name="FinSet"><span class="id" title="constructor">FinSet</span></a> <span class="id" title="keyword">of</span> <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="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.finset.html#SetType.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finfun.html#31493a873acc18a8368490ef56022c0c"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="finfun_of_set"><span class="id" title="definition">finfun_of_set</span></a> <span class="id" title="var">A</span> := <span class="id" title="keyword">let</span>: <a class="idref" href="mathcomp.ssreflect.finset.html#FinSet"><span class="id" title="constructor">FinSet</span></a> <span class="id" title="var">f</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">f</span>.<br/> -<span class="id" title="keyword">Definition</span> <a name="set_of"><span class="id" title="definition">set_of</span></a> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#SetType.T"><span class="id" title="variable">T</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a>.<br/> -<span class="id" title="keyword">Identity</span> <span class="id" title="keyword">Coercion</span> <span class="id" title="var">type_of_set_of</span> : <span class="id" title="var">set_of</span> >-> <span class="id" title="var">set_type</span>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_subType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#685b4c9ab7ccde70d9229dfbdb93d490"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#685b4c9ab7ccde70d9229dfbdb93d490"><span class="id" title="notation">newType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#685b4c9ab7ccde70d9229dfbdb93d490"><span class="id" title="notation">for</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#finfun_of_set"><span class="id" title="definition">finfun_of_set</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#685b4c9ab7ccde70d9229dfbdb93d490"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="set_eqMixin"><span class="id" title="definition">set_eqMixin</span></a> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">eqMixin</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#b361a0fe0b43cea5c506ee5eccc55542"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_eqType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.EqType"><span class="id" title="abbreviation">EqType</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_eqMixin"><span class="id" title="definition">set_eqMixin</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="set_choiceMixin"><span class="id" title="definition">set_choiceMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">choiceMixin</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#035054ba987e1c05f2985518b41ec31f"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_choiceType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#Choice.Exports.ChoiceType"><span class="id" title="abbreviation">ChoiceType</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_choiceMixin"><span class="id" title="definition">set_choiceMixin</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="set_countMixin"><span class="id" title="definition">set_countMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">countMixin</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#c2a823e7a76d1d303efdd00309d93aca"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_countType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#Countable.Exports.CountType"><span class="id" title="abbreviation">CountType</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_countMixin"><span class="id" title="definition">set_countMixin</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_subCountType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">subCountType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="set_finMixin"><span class="id" title="definition">set_finMixin</span></a> := <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">finMixin</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation">by</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#fede21e6a36088be0833d2600143b39c"><span class="id" title="notation"><:]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_finType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</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.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_finMixin"><span class="id" title="definition">set_finMixin</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_subFinType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">subFinType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#SetType"><span class="id" title="section">SetType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Delimit</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">set_scope</span> <span class="id" title="keyword">with</span> <span class="id" title="var">SET</span>.<br/> -<span class="id" title="keyword">Open</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">set_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">"</span></a>{ 'set' T }" := (<a class="idref" href="mathcomp.ssreflect.finset.html#set_of"><span class="id" title="definition">set_of</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">T</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "{ 'set' T }") : <span class="id" title="var">type_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - We later define several subtypes that coerce to set; for these it is - preferable to state equalities at the {set _} level, even when comparing - subtype values, because the primitive "injection" tactic tends to diverge - on complex types (e.g., quotient groups). We provide some parse-only - notation to make this technicality less obstrusive. -</div> -<div class="code"> -<span class="id" title="keyword">Notation</span> <a name="f0bbce9238fab3dd03626439080979a9"><span class="id" title="notation">"</span></a>A :=: B" := (<span class="id" title="var">A</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> <span class="id" title="var">B</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c6306907993ec830e8152150c233ecd3"><span class="id" title="notation">"</span></a>A :<>: B" := (<span class="id" title="var">A</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6583af5dff6354b395a20142a952fac3"><span class="id" title="notation">≠</span></a> <span class="id" title="var">B</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#6583af5dff6354b395a20142a952fac3"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="b91223a7636398c530555b2312d1e79b"><span class="id" title="notation">"</span></a>A :==: B" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#28a3089bb29d95d7bdc98c2c73b31552"><span class="id" title="notation">==</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#28a3089bb29d95d7bdc98c2c73b31552"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="be2f022a539ec6d4d51932b5ea998e57"><span class="id" title="notation">"</span></a>A :!=: B" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#228e85e3c31a939cba019f255574c875"><span class="id" title="notation">!=</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#228e85e3c31a939cba019f255574c875"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="57d7a7877432f8e19c5f82298a22b80a"><span class="id" title="notation">"</span></a>A :=P: B" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#4bd3c31686439006664c658ab8fdfe4e"><span class="id" title="notation">=</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#4bd3c31686439006664c658ab8fdfe4e"><span class="id" title="notation">P</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#4bd3c31686439006664c658ab8fdfe4e"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 70, <span class="id" title="keyword">no</span> <span class="id" title="keyword">associativity</span>, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Type</span> <a name="SetDefSig"><span class="id" title="module">SetDefSig</span></a>.<br/> -<span class="id" title="keyword">Parameter</span> <a name="SetDefSig.finset"><span class="id" title="axiom">finset</span></a> : <span class="id" title="keyword">∀</span> <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="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.finset.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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Parameter</span> <a name="SetDefSig.pred_of_set"><span class="id" title="axiom">pred_of_set</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">T</span>, <a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.fintype.html#fin_pred_sort"><span class="id" title="definition">fin_pred_sort</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#predPredType"><span class="id" title="definition">predPredType</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a>).<br/> -</div> - -<div class="doc"> - The weird type of pred_of_set is imposed by the syntactic restrictions on - coercion declarations; it is unfortunately not possible to use a functor - to retype the declaration, because this triggers an ugly bug in the Coq - coercion chaining code. -</div> -<div class="code"> -<span class="id" title="keyword">Axiom</span> <a name="SetDefSig.finsetE"><span class="id" title="axiom">finsetE</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#SetDefSig.finset"><span class="id" title="axiom">finset</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.finset.html#finset_def"><span class="id" title="abbreviation">finset_def</span></a>.<br/> -<span class="id" title="keyword">Axiom</span> <a name="SetDefSig.pred_of_setE"><span class="id" title="axiom">pred_of_setE</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#SetDefSig.pred_of_set"><span class="id" title="axiom">pred_of_set</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.finset.html#pred_of_set_def"><span class="id" title="abbreviation">pred_of_set_def</span></a>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#SetDefSig"><span class="id" title="module">SetDefSig</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="SetDef"><span class="id" title="module">SetDef</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#SetDefSig"><span class="id" title="module">SetDefSig</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="SetDef.finset"><span class="id" title="definition">finset</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#finset_def"><span class="id" title="abbreviation">finset_def</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="SetDef.pred_of_set"><span class="id" title="definition">pred_of_set</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set_def"><span class="id" title="abbreviation">pred_of_set_def</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="SetDef.finsetE"><span class="id" title="lemma">finsetE</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#SetDef.finset"><span class="id" title="definition">finset</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.finset.html#finset_def"><span class="id" title="abbreviation">finset_def</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="SetDef.pred_of_setE"><span class="id" title="lemma">pred_of_setE</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#SetDef.pred_of_set"><span class="id" title="definition">pred_of_set</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.finset.html#pred_of_set_def"><span class="id" title="abbreviation">pred_of_set_def</span></a>. <br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#SetDef"><span class="id" title="module">SetDef</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="finset"><span class="id" title="abbreviation">finset</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#finset"><span class="id" title="axiom">SetDef.finset</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="pred_of_set"><span class="id" title="abbreviation">pred_of_set</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="axiom">SetDef.pred_of_set</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">finset_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.finset.html#finsetE"><span class="id" title="axiom">SetDef.finsetE</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">pred_of_set_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.finset.html#pred_of_setE"><span class="id" title="axiom">SetDef.pred_of_setE</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">"</span></a>[ 'set' x : T | P ]" := (<a class="idref" href="mathcomp.ssreflect.finset.html#finset"><span class="id" title="abbreviation">finset</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> : <span class="id" title="var">T</span> ⇒ <span class="id" title="var">P</span>%<span class="id" title="var">B</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">"</span></a>[ 'set' x | P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span>, <span class="id" title="var">P</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span> "[ 'set' x | P ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">"</span></a>[ 'set' x 'in' A ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <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> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span> "[ 'set' x 'in' A ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="99b986d0578a6faf1a7d67bf3ddfa2a7"><span class="id" title="notation">"</span></a>[ 'set' x : T 'in' A ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <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> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3e9d12914c7607378976c499a50a47c7"><span class="id" title="notation">"</span></a>[ 'set' x : T | P & Q ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span> <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> <span class="id" title="var">Q</span><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">"</span></a>[ 'set' x | P & Q ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span> <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> <span class="id" title="var">Q</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span>, <span class="id" title="var">P</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span> "[ 'set' x | P & Q ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">"</span></a>[ 'set' x : T 'in' A | P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#3e9d12914c7607378976c499a50a47c7"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3e9d12914c7607378976c499a50a47c7"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3e9d12914c7607378976c499a50a47c7"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3e9d12914c7607378976c499a50a47c7"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <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> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3e9d12914c7607378976c499a50a47c7"><span class="id" title="notation">&</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#3e9d12914c7607378976c499a50a47c7"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">"</span></a>[ 'set' x 'in' A | P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <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> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">&</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span> "[ 'set' x 'in' A | P ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a93a32dfa8c6b39f45b95dc0c4090231"><span class="id" title="notation">"</span></a>[ 'set' x 'in' A | P & Q ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span> <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> <span class="id" title="var">Q</span><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99,<br/> - <span class="id" title="var">format</span> "[ 'set' x 'in' A | P & Q ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="5fedda87beb76d00225125bcd57acdb8"><span class="id" title="notation">"</span></a>[ 'set' x : T 'in' A | P & Q ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span> <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> <span class="id" title="var">Q</span><a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - This lets us use set and subtypes of set, like group or coset_of, both as - collective predicates and as arguments of the \pi(_) notation. -</div> -<div class="code"> -<span class="id" title="keyword">Coercion</span> <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="axiom">pred_of_set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="axiom">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="axiom">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="axiom">>-></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="axiom">fin_pred_sort</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Declare pred_of_set as a canonical instance of topred, but use the - coercion to resolve mem A to @mem (predPredType T) (pred_of_set A). -</div> -<div class="code"> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_predType</span> <span class="id" title="var">T</span> := @<a class="idref" href="mathcomp.ssreflect.ssrbool.html#PredType"><span class="id" title="definition">PredType</span></a> <span class="id" title="var">_</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#unkeyed"><span class="id" title="abbreviation">unkeyed</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#set_type"><span class="id" title="inductive">set_type</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a>)) (@<a class="idref" href="mathcomp.ssreflect.finset.html#pred_of_set"><span class="id" title="abbreviation">pred_of_set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="BasicSetTheory"><span class="id" title="section">BasicSetTheory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="BasicSetTheory.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">pA</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.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_of_subType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#aa8c179e7d847b79500c7558a661edb0"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#aa8c179e7d847b79500c7558a661edb0"><span class="id" title="notation">subType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#aa8c179e7d847b79500c7558a661edb0"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#aa8c179e7d847b79500c7558a661edb0"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_of_eqType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">eqType</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#2b9222c46a529018a8ebb5be6355801c"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_of_choiceType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">choiceType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#6cecb3ca492751e55998eec154506328"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_of_countType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#3fd72847645c366340e6e9be05776bd8"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#3fd72847645c366340e6e9be05776bd8"><span class="id" title="notation">countType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#3fd72847645c366340e6e9be05776bd8"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#3fd72847645c366340e6e9be05776bd8"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_of_subCountType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">subCountType</span></a> <a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.choice.html#9bbd910cbebcec91f8279b0711b4702d"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_of_finType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#0e3773306b0834fa9a0572c7b198b77f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#0e3773306b0834fa9a0572c7b198b77f"><span class="id" title="notation">finType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#0e3773306b0834fa9a0572c7b198b77f"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#0e3773306b0834fa9a0572c7b198b77f"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">set_of_subFinType</span> := <span class="id" title="keyword">Eval</span> <span class="id" title="tactic">hnf</span> <span class="id" title="tactic">in</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">subFinType</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">of</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#ea70e506e168d39ce0ec3d3ecd2c349f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_set"><span class="id" title="lemma">in_set</span></a> <span class="id" title="var">pA</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#finset"><span class="id" title="abbreviation">finset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</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.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setP"><span class="id" title="lemma">setP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#4bfb4f2d0721ba668e3a802ab1b745a1"><span class="id" title="notation">↔</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="set0"><span class="id" title="definition">set0</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><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.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="setTfor"><span class="id" title="definition">setTfor</span></a> (<span class="id" title="var">phT</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#phant"><span class="id" title="inductive">phant</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a>) := <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><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.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setT"><span class="id" title="lemma">in_setT</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#setTfor"><span class="id" title="definition">setTfor</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eqsVneq"><span class="id" title="lemma">eqsVneq</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.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span class="id" title="notation">}</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span class="id" title="notation">+</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_finset"><span class="id" title="lemma">eq_finset</span></a> (<span class="id" title="var">pA</span> <span class="id" title="var">pB</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.finset.html#BasicSetTheory.T"><span class="id" title="variable">T</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</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.finset.html#pB"><span class="id" title="variable">pB</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.finset.html#finset"><span class="id" title="abbreviation">finset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</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.finset.html#finset"><span class="id" title="abbreviation">finset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pB"><span class="id" title="variable">pB</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#BasicSetTheory"><span class="id" title="section">BasicSetTheory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="inE"><span class="id" title="definition">inE</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.finset.html#in_set"><span class="id" title="lemma">in_set</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#inE"><span class="id" title="definition">inE</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">Hint Resolve</span> <span class="id" title="var">in_setT</span> : <span class="id" title="var">core</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">"</span></a>[ 'set' : T ]" := (<a class="idref" href="mathcomp.ssreflect.finset.html#setTfor"><span class="id" title="definition">setTfor</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#Phant"><span class="id" title="constructor">Phant</span></a> <span class="id" title="var">T</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">format</span> "[ 'set' : T ]") : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="setT"><span class="id" title="abbreviation">setT</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">]</span></a> (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>).<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="setOpsDefs"><span class="id" title="section">setOpsDefs</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="setOpsDefs.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsDefs.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsDefs.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">P</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsDefs.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="set1"><span class="id" title="definition">set1</span></a> <span class="id" title="var">a</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="setU"><span class="id" title="definition">setU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="setC"><span class="id" title="definition">setC</span></a> <span class="id" title="var">A</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="setD"><span class="id" title="definition">setD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="ssetI"><span class="id" title="definition">ssetI</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="powerset"><span class="id" title="definition">powerset</span></a> <span class="id" title="var">D</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsDefs.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsDefs"><span class="id" title="section">setOpsDefs</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">"</span></a>[ 'set' a ]" := (<a class="idref" href="mathcomp.ssreflect.finset.html#set1"><span class="id" title="definition">set1</span></a> <span class="id" title="var">a</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span> "[ 'set' a ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="6d2e06e8091bd5b9f5e7d35d5cd348ac"><span class="id" title="notation">"</span></a>[ 'set' a : T ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">(</span></a><span class="id" title="var">a</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#aed478b27f23b4f753c27c8ac393febc"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">)]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span> "[ 'set' a : T ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">"</span></a>A :|: B" := (<a class="idref" href="mathcomp.ssreflect.finset.html#setU"><span class="id" title="definition">setU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">"</span></a>a |: A" := (<a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <span class="id" title="var">A</span>) : <span class="id" title="var">set_scope</span>.<br/> -</div> - -<div class="doc"> - This is left-associative due to historical limitations of the .. Notation. -</div> -<div class="code"> -<span class="id" title="keyword">Notation</span> <a name="f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">"</span></a>[ 'set' a1 ; a2 ; .. ; an ]" := (<a class="idref" href="mathcomp.ssreflect.finset.html#setU"><span class="id" title="definition">setU</span></a> .. (<span class="id" title="var">a1</span> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a2</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>) .. <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">an</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">a1</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99,<br/> - <span class="id" title="var">format</span> "[ 'set' a1 ; a2 ; .. ; an ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">"</span></a>A :&: B" := (<a class="idref" href="mathcomp.ssreflect.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">"</span></a>~: A" := (<a class="idref" href="mathcomp.ssreflect.finset.html#setC"><span class="id" title="definition">setC</span></a> <span class="id" title="var">A</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 35, <span class="id" title="tactic">right</span> <span class="id" title="keyword">associativity</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">"</span></a>[ 'set' ~ a ]" := (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</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> "[ 'set' ~ a ]") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">"</span></a>A :\: B" := (<a class="idref" href="mathcomp.ssreflect.finset.html#setD"><span class="id" title="definition">setD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">"</span></a>A :\ a" := (<span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">a</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="7ed77f64965385480255328de15d774c"><span class="id" title="notation">"</span></a>P ::&: D" := (<a class="idref" href="mathcomp.ssreflect.finset.html#ssetI"><span class="id" title="definition">ssetI</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 48) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="setOps"><span class="id" title="section">setOps</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="setOps.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">a</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">pA</span> <span class="id" title="var">pB</span> <span class="id" title="var">pC</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.finset.html#setOps.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eqEsubset"><span class="id" title="lemma">eqEsubset</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subEproper"><span class="id" title="lemma">subEproper</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eqVproper"><span class="id" title="lemma">eqVproper</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#f031fe1957c4a4a8e217aa46af2b4e25"><span class="id" title="notation">∨</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properEneq"><span class="id" title="lemma">properEneq</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="proper_neq"><span class="id" title="lemma">proper_neq</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eqEproper"><span class="id" title="lemma">eqEproper</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b3ebd0deddd84fd60e149cb5ef719351"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eqEcard"><span class="id" title="lemma">eqEcard</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#cb53cf0ee22c036a03b4a9281c68b5a3"><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.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properEcard"><span class="id" title="lemma">properEcard</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#00fe0eaf5e6949f0a31725357afa4bba"><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.finset.html#B"><span class="id" title="variable">B</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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subset_leqif_cards"><span class="id" title="lemma">subset_leqif_cards</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#22d09a36997010daec8f30c044c9e5d4"><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.finset.html#B"><span class="id" title="variable">B</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#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.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#22d09a36997010daec8f30c044c9e5d4"><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/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_set0"><span class="id" title="lemma">in_set0</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#set0"><span class="id" title="definition">set0</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.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sub0set"><span class="id" title="lemma">sub0set</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subset0"><span class="id" title="lemma">subset0</span></a> <span class="id" title="var">A</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="proper0"><span class="id" title="lemma">proper0</span></a> <span class="id" title="var">A</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.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="subset_neq0"><span class="id" title="lemma">subset_neq0</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set_0Vmem"><span class="id" title="lemma">set_0Vmem</span></a> <span class="id" title="var">A</span> : <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.finset.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.finset.html#set0"><span class="id" title="definition">set0</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="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="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">x</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.finset.html#setOps.T"><span class="id" title="variable">T</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.finset.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.finset.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#6556914db359db999889decec6a4a562"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="enum_set0"><span class="id" title="lemma">enum_set0</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.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><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.finset.html#setOps.T"><span class="id" title="variable">T</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetT"><span class="id" title="lemma">subsetT</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetT_hint"><span class="id" title="lemma">subsetT_hint</span></a> <span class="id" title="var">mA</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#SubsetDef.subset"><span class="id" title="axiom">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#mA"><span class="id" title="variable">mA</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">]</span></a>).<br/> - <span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">subsetT_hint</span> : <span class="id" title="var">core</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subTset"><span class="id" title="lemma">subTset</span></a> <span class="id" title="var">A</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.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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="properT"><span class="id" title="lemma">properT</span></a> <span class="id" title="var">A</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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="set1P"><span class="id" title="lemma">set1P</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> : <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> (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#a"><span class="id" title="variable">a</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="enum_setT"><span class="id" title="lemma">enum_setT</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.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><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.fintype.html#Finite.enum"><span class="id" title="abbreviation">Finite.enum</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_set1"><span class="id" title="lemma">in_set1</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</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.finset.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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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="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.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set11"><span class="id" title="lemma">set11</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set1_inj"><span class="id" title="lemma">set1_inj</span></a> : <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.finset.html#set1"><span class="id" title="definition">set1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="enum_set1"><span class="id" title="lemma">enum_set1</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#enum"><span class="id" title="abbreviation">enum</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">[::</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.seq.html#506674b18256ef8f50efed43fa1dfd7d"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setU1P"><span class="id" title="lemma">setU1P</span></a> <span class="id" title="var">x</span> <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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#f031fe1957c4a4a8e217aa46af2b4e25"><span class="id" title="notation">∨</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setU1"><span class="id" title="lemma">in_setU1</span></a> <span class="id" title="var">x</span> <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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set_cons"><span class="id" title="lemma">set_cons</span></a> <span class="id" title="var">a</span> <span class="id" title="var">s</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.seq.html#407cde5b61fbf27196d1a7c5a475e083"><span class="id" title="notation">::</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#s"><span class="id" title="variable">s</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><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.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#s"><span class="id" title="variable">s</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setU11"><span class="id" title="lemma">setU11</span></a> <span class="id" title="var">x</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setU1r"><span class="id" title="lemma">setU1r</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</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.finset.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.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - We need separate lemmas for the explicit enumerations since they - associate on the left. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="set1Ul"><span class="id" title="lemma">set1Ul</span></a> <span class="id" title="var">x</span> <span class="id" title="var">A</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set1Ur"><span class="id" title="lemma">set1Ur</span></a> <span class="id" title="var">A</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setC1"><span class="id" title="lemma">in_setC1</span></a> <span class="id" title="var">x</span> <span class="id" title="var">a</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.finset.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.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">¬</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><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="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.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setC11"><span class="id" title="lemma">setC11</span></a> <span class="id" title="var">x</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.finset.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.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">¬</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><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="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.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setD1P"><span class="id" title="lemma">setD1P</span></a> <span class="id" title="var">x</span> <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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setD1"><span class="id" title="lemma">in_setD1</span></a> <span class="id" title="var">x</span> <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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</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="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.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</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="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.finset.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.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a> .<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setD11"><span class="id" title="lemma">setD11</span></a> <span class="id" title="var">b</span> <span class="id" title="var">A</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.finset.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#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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#false"><span class="id" title="constructor">false</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setD1K"><span class="id" title="lemma">setD1K</span></a> <span class="id" title="var">a</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setU1K"><span class="id" title="lemma">setU1K</span></a> <span class="id" title="var">a</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set2P"><span class="id" title="lemma">set2P</span></a> <span class="id" title="var">x</span> <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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#f031fe1957c4a4a8e217aa46af2b4e25"><span class="id" title="notation">∨</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#b"><span class="id" title="variable">b</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">]</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_set2"><span class="id" title="lemma">in_set2</span></a> <span class="id" title="var">x</span> <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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><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="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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set21"><span class="id" title="lemma">set21</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set22"><span class="id" title="lemma">set22</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUP"><span class="id" title="lemma">setUP</span></a> <span class="id" title="var">x</span> <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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#f031fe1957c4a4a8e217aa46af2b4e25"><span class="id" title="notation">∨</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setU"><span class="id" title="lemma">in_setU</span></a> <span class="id" title="var">x</span> <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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUC"><span class="id" title="lemma">setUC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUS"><span class="id" title="lemma">setUS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setSU"><span class="id" title="lemma">setSU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUSS"><span class="id" title="lemma">setUSS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set0U"><span class="id" title="lemma">set0U</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setU0"><span class="id" title="lemma">setU0</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUA"><span class="id" title="lemma">setUA</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUCA"><span class="id" title="lemma">setUCA</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUAC"><span class="id" title="lemma">setUAC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUACA"><span class="id" title="lemma">setUACA</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setTU"><span class="id" title="lemma">setTU</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUT"><span class="id" title="lemma">setUT</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUid"><span class="id" title="lemma">setUid</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUUl"><span class="id" title="lemma">setUUl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUUr"><span class="id" title="lemma">setUUr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - intersection -<div class="paragraph"> </div> - - setIdP is a generalisation of setIP that applies to comprehensions. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="setIdP"><span class="id" title="lemma">setIdP</span></a> <span class="id" title="var">x</span> <span class="id" title="var">pA</span> <span class="id" title="var">pB</span> : <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> (<a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pB"><span class="id" title="variable">pB</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pB"><span class="id" title="variable">pB</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">]</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setId2P"><span class="id" title="lemma">setId2P</span></a> <span class="id" title="var">x</span> <span class="id" title="var">pA</span> <span class="id" title="var">pB</span> <span class="id" title="var">pC</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> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">[/\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pB"><span class="id" title="variable">pB</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pC"><span class="id" title="variable">pC</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#d7e433f5d2fe56f5b712860a9ff2a681"><span class="id" title="notation">]</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pB"><span class="id" title="variable">pB</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">&&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pC"><span class="id" title="variable">pC</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">]</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIdE"><span class="id" title="lemma">setIdE</span></a> <span class="id" title="var">A</span> <span class="id" title="var">pB</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pB"><span class="id" title="variable">pB</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pB"><span class="id" title="variable">pB</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIP"><span class="id" title="lemma">setIP</span></a> <span class="id" title="var">x</span> <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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setI"><span class="id" title="lemma">in_setI</span></a> <span class="id" title="var">x</span> <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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.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.finset.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.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="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.finset.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.finset.html#B"><span class="id" title="variable">B</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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIC"><span class="id" title="lemma">setIC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIS"><span class="id" title="lemma">setIS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setSI"><span class="id" title="lemma">setSI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setISS"><span class="id" title="lemma">setISS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setTI"><span class="id" title="lemma">setTI</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIT"><span class="id" title="lemma">setIT</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set0I"><span class="id" title="lemma">set0I</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setI0"><span class="id" title="lemma">setI0</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIA"><span class="id" title="lemma">setIA</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setICA"><span class="id" title="lemma">setICA</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIAC"><span class="id" title="lemma">setIAC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIACA"><span class="id" title="lemma">setIACA</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIid"><span class="id" title="lemma">setIid</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIIl"><span class="id" title="lemma">setIIl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIIr"><span class="id" title="lemma">setIIr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - distribute /cancel -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIUr"><span class="id" title="lemma">setIUr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIUl"><span class="id" title="lemma">setIUl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUIr"><span class="id" title="lemma">setUIr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUIl"><span class="id" title="lemma">setUIl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUK"><span class="id" title="lemma">setUK</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setKU"><span class="id" title="lemma">setKU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIK"><span class="id" title="lemma">setIK</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setKI"><span class="id" title="lemma">setKI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - complement -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setCP"><span class="id" title="lemma">setCP</span></a> <span class="id" title="var">x</span> <span class="id" title="var">A</span> : <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> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#63a68285c81db8f9bc456233bb9ed181"><span class="id" title="notation">¬</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setC"><span class="id" title="lemma">in_setC</span></a> <span class="id" title="var">x</span> <span class="id" title="var">A</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.finset.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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setCK"><span class="id" title="lemma">setCK</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#involutive"><span class="id" title="definition">involutive</span></a> (@<a class="idref" href="mathcomp.ssreflect.finset.html#setC"><span class="id" title="definition">setC</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setC_inj"><span class="id" title="lemma">setC_inj</span></a> : <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.finset.html#setC"><span class="id" title="definition">setC</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsets_disjoint"><span class="id" title="lemma">subsets_disjoint</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.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.finset.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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="disjoints_subset"><span class="id" title="lemma">disjoints_subset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <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.finset.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.finset.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#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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="powersetCE"><span class="id" title="lemma">powersetCE</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#powerset"><span class="id" title="definition">powerset</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.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.finset.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.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setCS"><span class="id" title="lemma">setCS</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setCU"><span class="id" title="lemma">setCU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setCI"><span class="id" title="lemma">setCI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUCr"><span class="id" title="lemma">setUCr</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setICr"><span class="id" title="lemma">setICr</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setC0"><span class="id" title="lemma">setC0</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setCT"><span class="id" title="lemma">setCT</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - difference -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDP"><span class="id" title="lemma">setDP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">x</span> : <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> (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setD"><span class="id" title="lemma">in_setD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">x</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.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.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.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDE"><span class="id" title="lemma">setDE</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setSD"><span class="id" title="lemma">setSD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDS"><span class="id" title="lemma">setDS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDSS"><span class="id" title="lemma">setDSS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setD0"><span class="id" title="lemma">setD0</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set0D"><span class="id" title="lemma">set0D</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDT"><span class="id" title="lemma">setDT</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setTD"><span class="id" title="lemma">setTD</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDv"><span class="id" title="lemma">setDv</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setCD"><span class="id" title="lemma">setCD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setID"><span class="id" title="lemma">setID</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDUl"><span class="id" title="lemma">setDUl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDUr"><span class="id" title="lemma">setDUr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDIl"><span class="id" title="lemma">setDIl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIDA"><span class="id" title="lemma">setIDA</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><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.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIDAC"><span class="id" title="lemma">setIDAC</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDIr"><span class="id" title="lemma">setDIr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDDl"><span class="id" title="lemma">setDDl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDDr"><span class="id" title="lemma">setDDr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - powerset -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="powersetE"><span class="id" title="lemma">powersetE</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="powersetS"><span class="id" title="lemma">powersetS</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="powerset0"><span class="id" title="lemma">powerset0</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="powersetT"><span class="id" title="lemma">powersetT</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><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.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setI_powerset"><span class="id" title="lemma">setI_powerset</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#7ed77f64965385480255328de15d774c"><span class="id" title="notation">::&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - cardinal lemmas for sets -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsE"><span class="id" title="lemma">cardsE</span></a> <span class="id" title="var">pA</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><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.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.finset.html#pA"><span class="id" title="variable">pA</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="sum1dep_card"><span class="id" title="lemma">sum1dep_card</span></a> <span class="id" title="var">pA</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#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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><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.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><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="sum_nat_cond_const"><span class="id" title="lemma">sum_nat_cond_const</span></a> <span class="id" title="var">pA</span> <span class="id" title="var">n</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#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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#490a7188a07350a81d958e0206419577"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pA"><span class="id" title="variable">pA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#9e3f1d0cf47c39e3927b1f03a0797327"><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.ssrnat.html#ea2ff3d561159081cea6fb2e8113cc54"><span class="id" title="notation">×</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#n"><span class="id" title="variable">n</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cards0"><span class="id" title="lemma">cards0</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a>@<a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</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> 0.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cards_eq0"><span class="id" title="lemma">cards_eq0</span></a> <span class="id" title="var">A</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#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><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#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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="set0Pn"><span class="id" title="lemma">set0Pn</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">x</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="card_gt0"><span class="id" title="lemma">card_gt0</span></a> <span class="id" title="var">A</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>0 <a class="idref" href="mathcomp.ssreflect.ssrnat.html#00fe0eaf5e6949f0a31725357afa4bba"><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.finset.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> <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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="cards0_eq"><span class="id" title="lemma">cards0_eq</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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> 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="mathcomp.ssreflect.finset.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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cards1"><span class="id" title="lemma">cards1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> 1.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsUI"><span class="id" title="lemma">cardsUI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#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="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#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="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="cardsU"><span class="id" title="lemma">cardsU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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> (<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#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="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#7825ccc99f23b0d30c9d40c317ba7af0"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsI"><span class="id" title="lemma">cardsI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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> (<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#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="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#7825ccc99f23b0d30c9d40c317ba7af0"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsT"><span class="id" title="lemma">cardsT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d1cce020b4b43370087fd70de1477ab6"><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.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.finset.html#setOps.T"><span class="id" title="variable">T</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="cardsID"><span class="id" title="lemma">cardsID</span></a> <span class="id" title="var">B</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#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="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsD"><span class="id" title="lemma">cardsD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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> (<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#7825ccc99f23b0d30c9d40c317ba7af0"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsC"><span class="id" title="lemma">cardsC</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#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="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</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="cardsCs"><span class="id" title="lemma">cardsCs</span></a> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setOps.T"><span class="id" title="variable">T</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#7825ccc99f23b0d30c9d40c317ba7af0"><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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsU1"><span class="id" title="lemma">cardsU1</span></a> <span class="id" title="var">a</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">)</span></a> <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="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cards2"><span class="id" title="lemma">cards2</span></a> <span class="id" title="var">a</span> <span class="id" title="var">b</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#bda89d73ec4a8f23ae92b565ffb5aaa6"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b"><span class="id" title="variable">b</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="cardsC1"><span class="id" title="lemma">cardsC1</span></a> <span class="id" title="var">a</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">set</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><span class="id" title="notation">¬</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f4a9366aacdc0a2f03cd10ba6ee550fb"><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.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.finset.html#setOps.T"><span class="id" title="variable">T</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#f953bf7095e0da1cb644443fd0e17d6d"><span class="id" title="notation">.-1</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsD1"><span class="id" title="lemma">cardsD1</span></a> <span class="id" title="var">a</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.ssrnat.html#0dacc1786c5ba797d47dd85006231633"><span class="id" title="notation">)</span></a> <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="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -</div> - -<div class="doc"> - other inclusions -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetIl"><span class="id" title="lemma">subsetIl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetIr"><span class="id" title="lemma">subsetIr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetUl"><span class="id" title="lemma">subsetUl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetUr"><span class="id" title="lemma">subsetUr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetU1"><span class="id" title="lemma">subsetU1</span></a> <span class="id" title="var">x</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetDl"><span class="id" title="lemma">subsetDl</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subD1set"><span class="id" title="lemma">subD1set</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetDr"><span class="id" title="lemma">subsetDr</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sub1set"><span class="id" title="lemma">sub1set</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.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.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cards1P"><span class="id" title="lemma">cards1P</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">x</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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.finset.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.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subset1"><span class="id" title="lemma">subset1</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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="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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="powerset1"><span class="id" title="lemma">powerset1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">;</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f714e54c16ed806ac79437fa972e90ff"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIidPl"><span class="id" title="lemma">setIidPl</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setIidPr"><span class="id" title="lemma">setIidPr</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsDS"><span class="id" title="lemma">cardsDS</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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> (<a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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#7825ccc99f23b0d30c9d40c317ba7af0"><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.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>)%<span class="id" title="var">N</span>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUidPl"><span class="id" title="lemma">setUidPl</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setUidPr"><span class="id" title="lemma">setUidPr</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setDidPl"><span class="id" title="lemma">setDidPl</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.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.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">disjoint</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subIset"><span class="id" title="lemma">subIset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetI"><span class="id" title="lemma">subsetI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetIP"><span class="id" title="lemma">subsetIP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetIidl"><span class="id" title="lemma">subsetIidl</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="subsetIidr"><span class="id" title="lemma">subsetIidr</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="powersetI"><span class="id" title="lemma">powersetI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subUset"><span class="id" title="lemma">subUset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.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="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.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetU"><span class="id" title="lemma">subsetU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subUsetP"><span class="id" title="lemma">subUsetP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</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#reflect"><span class="id" title="abbreviation">reflect</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetC"><span class="id" title="lemma">subsetC</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subCset"><span class="id" title="lemma">subCset</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetD"><span class="id" title="lemma">subsetD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.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.finset.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.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subDset"><span class="id" title="lemma">subDset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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="subsetDP"><span class="id" title="lemma">subsetDP</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <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.finset.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.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">]</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setU_eq0"><span class="id" title="lemma">setU_eq0</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setD_eq0"><span class="id" title="lemma">setD_eq0</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="setI_eq0"><span class="id" title="lemma">setI_eq0</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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.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.finset.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.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="disjoint_setI0"><span class="id" title="lemma">disjoint_setI0</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <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.finset.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.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetD1"><span class="id" title="lemma">subsetD1</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">x</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="subsetD1P"><span class="id" title="lemma">subsetD1P</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">x</span> : <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> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properD1"><span class="id" title="lemma">properD1</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properIr"><span class="id" title="lemma">properIr</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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properIl"><span class="id" title="lemma">properIl</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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properUr"><span class="id" title="lemma">properUr</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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properUl"><span class="id" title="lemma">properUl</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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b3ebd0deddd84fd60e149cb5ef719351"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="proper1set"><span class="id" title="lemma">proper1set</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</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><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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="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.finset.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.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properIset"><span class="id" title="lemma">properIset</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">||</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#081ff67d3116402bb680e8692aa39185"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#081ff67d3116402bb680e8692aa39185"><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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properI"><span class="id" title="lemma">properI</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properU"><span class="id" title="lemma">properU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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="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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.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="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.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#9ddeac0ab66152bd1d64bedb507a795e"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="properD"><span class="id" title="lemma">properD</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</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><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.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.finset.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.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#setOps"><span class="id" title="section">setOps</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Hint Resolve</span> <span class="id" title="var">subsetT_hint</span> : <span class="id" title="var">core</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="setOpsAlgebra"><span class="id" title="section">setOpsAlgebra</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">Variable</span> <a name="setOpsAlgebra.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setI_monoid</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.finset.html#setIA"><span class="id" title="lemma">setIA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#setTI"><span class="id" title="lemma">setTI</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#setIT"><span class="id" title="lemma">setIT</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setI_comoid</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.finset.html#setIC"><span class="id" title="lemma">setIC</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setI_muloid</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.finset.html#set0I"><span class="id" title="lemma">set0I</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#setI0"><span class="id" title="lemma">setI0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setU_monoid</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.finset.html#setUA"><span class="id" title="lemma">setUA</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#set0U"><span class="id" title="lemma">set0U</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#setU0"><span class="id" title="lemma">setU0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setU_comoid</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.finset.html#setUC"><span class="id" title="lemma">setUC</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setU_muloid</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.finset.html#setTU"><span class="id" title="lemma">setTU</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#setUT"><span class="id" title="lemma">setUT</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setI_addoid</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.finset.html#setUIl"><span class="id" title="lemma">setUIl</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#setUIr"><span class="id" title="lemma">setUIr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">setU_addoid</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.finset.html#setIUl"><span class="id" title="lemma">setIUl</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>) (@<a class="idref" href="mathcomp.ssreflect.finset.html#setIUr"><span class="id" title="lemma">setIUr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra.T"><span class="id" title="variable">T</span></a>).<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#setOpsAlgebra"><span class="id" title="section">setOpsAlgebra</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="CartesianProd"><span class="id" title="section">CartesianProd</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="CartesianProd.fT1"><span class="id" title="variable">fT1</span></a> <a name="CartesianProd.fT2"><span class="id" title="variable">fT2</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="CartesianProd.A1"><span class="id" title="variable">A1</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CartesianProd.fT1"><span class="id" title="variable">fT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="CartesianProd.A2"><span class="id" title="variable">A2</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CartesianProd.fT2"><span class="id" title="variable">fT2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="setX"><span class="id" title="definition">setX</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">set</span></a> <span class="id" title="var">u</span> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#u"><span class="id" title="variable">u</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.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.finset.html#CartesianProd.A1"><span class="id" title="variable">A1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#u"><span class="id" title="variable">u</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="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.finset.html#CartesianProd.A2"><span class="id" title="variable">A2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#4e173ac66c4bfb69f9f0316bf3f59a43"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="in_setX"><span class="id" title="lemma">in_setX</span></a> <span class="id" title="var">x1</span> <span class="id" title="var">x2</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="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.finset.html#x1"><span class="id" title="variable">x1</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.finset.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.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><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">\</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.finset.html#setX"><span class="id" title="definition">setX</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="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.finset.html#x1"><span class="id" title="variable">x1</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.finset.html#CartesianProd.A1"><span class="id" title="variable">A1</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="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.finset.html#x2"><span class="id" title="variable">x2</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.finset.html#CartesianProd.A2"><span class="id" title="variable">A2</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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setXP"><span class="id" title="lemma">setXP</span></a> <span class="id" title="var">x1</span> <span class="id" title="var">x2</span> : <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> (<a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</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.finset.html#CartesianProd.A1"><span class="id" title="variable">A1</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x2"><span class="id" title="variable">x2</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.finset.html#CartesianProd.A2"><span class="id" title="variable">A2</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.finset.html#x1"><span class="id" title="variable">x1</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.finset.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.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><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">\</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.finset.html#setX"><span class="id" title="definition">setX</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cardsX"><span class="id" title="lemma">cardsX</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setX"><span class="id" title="definition">setX</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#CartesianProd.A1"><span class="id" title="variable">A1</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.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#CartesianProd.A2"><span class="id" title="variable">A2</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">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#CartesianProd"><span class="id" title="section">CartesianProd</span></a>.<br/> - -<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Module</span> <span class="id" title="keyword">Type</span> <a name="ImsetSig"><span class="id" title="module">ImsetSig</span></a>.<br/> -<span class="id" title="keyword">Parameter</span> <a name="ImsetSig.imset"><span class="id" title="axiom">imset</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">aT</span> <span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</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.finset.html#aT"><span class="id" title="variable">aT</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.finset.html#rT"><span class="id" title="variable">rT</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem_pred"><span class="id" title="inductive">mem_pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#aT"><span class="id" title="variable">aT</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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Parameter</span> <a name="ImsetSig.imset2"><span class="id" title="axiom">imset2</span></a> : <span class="id" title="keyword">∀</span> <span class="id" title="var">aT1</span> <span class="id" title="var">aT2</span> <span class="id" title="var">rT</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</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.finset.html#aT1"><span class="id" title="variable">aT1</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.finset.html#aT2"><span class="id" title="variable">aT2</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.finset.html#rT"><span class="id" title="variable">rT</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem_pred"><span class="id" title="inductive">mem_pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#aT1"><span class="id" title="variable">aT1</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.finset.html#aT1"><span class="id" title="variable">aT1</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#mem_pred"><span class="id" title="inductive">mem_pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#aT2"><span class="id" title="variable">aT2</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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Axiom</span> <a name="ImsetSig.imsetE"><span class="id" title="axiom">imsetE</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetSig.imset"><span class="id" title="axiom">imset</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.finset.html#imset_def"><span class="id" title="abbreviation">imset_def</span></a>.<br/> -<span class="id" title="keyword">Axiom</span> <a name="ImsetSig.imset2E"><span class="id" title="axiom">imset2E</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetSig.imset2"><span class="id" title="axiom">imset2</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.finset.html#imset2_def"><span class="id" title="abbreviation">imset2_def</span></a>.<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetSig"><span class="id" title="module">ImsetSig</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Module</span> <a name="Imset"><span class="id" title="module">Imset</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetSig"><span class="id" title="module">ImsetSig</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="Imset.imset"><span class="id" title="definition">imset</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#imset_def"><span class="id" title="abbreviation">imset_def</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="Imset.imset2"><span class="id" title="definition">imset2</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#imset2_def"><span class="id" title="abbreviation">imset2_def</span></a>.<br/> -<span class="id" title="keyword">Lemma</span> <a name="Imset.imsetE"><span class="id" title="lemma">imsetE</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#Imset.imset"><span class="id" title="definition">imset</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.finset.html#imset_def"><span class="id" title="abbreviation">imset_def</span></a>. <br/> -<span class="id" title="keyword">Lemma</span> <a name="Imset.imset2E"><span class="id" title="lemma">imset2E</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#Imset.imset2"><span class="id" title="definition">imset2</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.finset.html#imset2_def"><span class="id" title="abbreviation">imset2_def</span></a>. <br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Imset"><span class="id" title="module">Imset</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="imset"><span class="id" title="abbreviation">imset</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#imset"><span class="id" title="axiom">Imset.imset</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="imset2"><span class="id" title="abbreviation">imset2</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="axiom">Imset.imset2</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">imset_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.finset.html#imsetE"><span class="id" title="axiom">Imset.imsetE</span></a>.<br/> -<span class="id" title="keyword">Canonical</span> <span class="id" title="var">imset2_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.finset.html#imset2E"><span class="id" title="axiom">Imset.imset2E</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="preimset"><span class="id" title="definition">preimset</span></a> (<span class="id" title="var">aT</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">rT</span> <span class="id" title="var">f</span> (<span class="id" title="var">R</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem_pred"><span class="id" title="inductive">mem_pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#rT"><span class="id" title="variable">rT</span></a>) :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#aT"><span class="id" title="variable">aT</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">|</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#in_mem"><span class="id" title="definition">in_mem</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#R"><span class="id" title="variable">R</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">"</span></a>f @^-1: A" := (<a class="idref" href="mathcomp.ssreflect.finset.html#preimset"><span class="id" title="definition">preimset</span></a> <span class="id" title="var">f</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>)) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 24) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">"</span></a>f @: A" := (<a class="idref" href="mathcomp.ssreflect.finset.html#imset"><span class="id" title="abbreviation">imset</span></a> <span class="id" title="var">f</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>)) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 24) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">"</span></a>f @2: ( A , B )" := (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> <span class="id" title="var">f</span> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">B</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 24, <span class="id" title="var">format</span> "f @2: ( A , B )") : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - Comprehensions -</div> -<div class="code"> -<span class="id" title="keyword">Notation</span> <a name="1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">"</span></a>[ 'set' E | x 'in' A ]" := (<a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> ⇒ <span class="id" title="var">E</span><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <span class="id" title="var">A</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99,<br/> - <span class="id" title="var">format</span> "[ '[hv' 'set' E '/ ' | x 'in' A ] ']'") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d0270fa0a363bba71e8c01890ad13e87"><span class="id" title="notation">"</span></a>[ 'set' E | x 'in' A & P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99,<br/> - <span class="id" title="var">format</span> "[ '[hv' 'set' E '/ ' | x 'in' A '/ ' & P ] ']'") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">"</span></a>[ 'set' E | x 'in' A , y 'in' B ]" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <span class="id" title="var">E</span>) (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> ⇒ (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">B</span>)))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'set' E '/ ' | x 'in' A , '/ ' y 'in' B ] ']'"<br/> - ) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="d2953ed2eddab96591880a46e5e8117b"><span class="id" title="notation">"</span></a>[ 'set' E | x 'in' A , y 'in' B & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'set' E '/ ' | x 'in' A , '/ ' y 'in' B '/ ' & P ] ']'"<br/> - ) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - Typed variants. -</div> -<div class="code"> -<span class="id" title="keyword">Notation</span> <a name="e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">"</span></a>[ 'set' E | x : T 'in' A ]" := (<a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> : <span class="id" title="var">T</span> ⇒ <span class="id" title="var">E</span><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <span class="id" title="var">A</span>)<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a6c7186a6a0433edd1ca6a38fcaf6356"><span class="id" title="notation">"</span></a>[ 'set' E | x : T 'in' A & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">"</span></a>[ 'set' E | x : T 'in' A , y : U 'in' B ]" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> (<span class="id" title="keyword">fun</span> (<span class="id" title="var">x</span> : <span class="id" title="var">T</span>) (<span class="id" title="var">y</span> : <span class="id" title="var">U</span>) ⇒ <span class="id" title="var">E</span>) (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>) (<span class="id" title="keyword">fun</span> (<span class="id" title="var">x</span> : <span class="id" title="var">T</span>) ⇒ (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">B</span>)))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="ba0daabfff15ad7e8dce828cc6273976"><span class="id" title="notation">"</span></a>[ 'set' E | x : T 'in' A , y : U 'in' B & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#5aaa2ecf7f1dd075658db9a82cd529e3"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - Comprehensions over a type. -</div> -<div class="code"> -<span class="id" title="keyword">Notation</span> <a name="2aea337939f802bdb1c1782cb3ee802b"><span class="id" title="notation">"</span></a>[ 'set' E | x : T ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#predOfType"><span class="id" title="abbreviation">predOfType</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99,<br/> - <span class="id" title="var">format</span> "[ '[hv' 'set' E '/ ' | x : T ] ']'") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="85a8a506c5f58a02f21729c9d8804acf"><span class="id" title="notation">"</span></a>[ 'set' E | x : T & P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">set</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#6ac1c202d9451e0a66d4fc93e5d9b44b"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#e3cc0bd99bb8cc63fd1c434164746477"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99,<br/> - <span class="id" title="var">format</span> "[ '[hv' 'set' E '/ ' | x : T '/ ' & P ] ']'") : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">"</span></a>[ 'set' E | x : T , y : U 'in' B ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#predOfType"><span class="id" title="abbreviation">predOfType</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'set' E '/ ' | x : T , '/ ' y : U 'in' B ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">"</span></a>[ 'set' E | x : T , y : U 'in' B & P ]" 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title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv ' 'set' E '/' | x : T , '/ ' y : U 'in' B '/' & P ] ']'"<br/> - ) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">"</span></a>[ 'set' E | x : T 'in' A , y : U ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#predOfType"><span class="id" title="abbreviation">predOfType</span></a> <span class="id" title="var">U</span><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'set' E '/ ' | x : T 'in' A , '/ ' y : U ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">"</span></a>[ 'set' E | x : T 'in' A , y : U & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">in</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#82a48e6d5f0b7f5617b486f4377ad839"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'set' E '/ ' | x : T 'in' A , '/ ' y : U & P ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">"</span></a>[ 'set' E | x : T , y : U ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#predOfType"><span class="id" title="abbreviation">predOfType</span></a> <span class="id" title="var">U</span><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'set' E '/ ' | x : T , '/ ' y : U ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">"</span></a>[ 'set' E | x : T , y : U & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">in</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'set' E '/ ' | x : T , '/ ' y : U & P ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - Untyped variants. -</div> -<div class="code"> -<span class="id" title="keyword">Notation</span> <a name="223afeb2a2b97fa949c188a9c6c59b20"><span class="id" title="notation">"</span></a>[ 'set' E | x , y 'in' B ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span><a class="idref" href="mathcomp.ssreflect.finset.html#ffefc3168943bb2f1e95b2a4a750130d"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="71d1fee89a0a034306ffd93ba6efd81d"><span class="id" title="notation">"</span></a>[ 'set' E | x , y 'in' B & P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">&</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#7e9f6fd8d4432053c2400bc73a2346b5"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="9341ed78b5ef484c91fec26f72458827"><span class="id" title="notation">"</span></a>[ 'set' E | x 'in' A , y ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#5d1fa0ea0beb5d1b1818120c68de35d6"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a6e39fc20ab018be7e5952aacce377bf"><span class="id" title="notation">"</span></a>[ 'set' E | x 'in' A , y & P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">&</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#7f52d1229fea47003e96d2aa48f36b0e"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3759f593b5fd7ef20d6372de49bdf3cf"><span class="id" title="notation">"</span></a>[ 'set' E | x , y ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#57dec0b78f559eebe12021ab4226ceca"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a18681f39140a291371b781af0d17795"><span class="id" title="notation">"</span></a>[ 'set' E | x , y & P ]" := <a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">set</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">:</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">&</span></a> <span class="id" title="var">P</span> <a class="idref" href="mathcomp.ssreflect.finset.html#e81e9fe993d33c973d7818fb420b6515"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -</div> - -<div class="doc"> - Print-only variants to work around the Coq pretty-printer K-term kink. -</div> -<div class="code"> -<span class="id" title="keyword">Notation</span> <a name="ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x 'in' A , y 'in' B ]" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <span class="id" title="var">E</span>) (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">B</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'se' 't' E '/ ' | x 'in' A , '/ ' y 'in' B ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3a177c5b6e45968947c8b4a3ebb1e064"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x 'in' A , y 'in' B & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">se</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">t</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">in</span></a> <span class="id" title="var">A</span><a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ebe59533658be38eae4d7c04870773fb"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv ' 'se' 't' E '/' | x 'in' A , '/ ' y 'in' B '/' & P ] ']'"<br/> - ) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x : T , y : U 'in' B ]" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> (<span class="id" title="var">y</span> : <span class="id" title="var">U</span>) ⇒ <span class="id" title="var">E</span>) (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#predOfType"><span class="id" title="abbreviation">predOfType</span></a> <span class="id" title="var">T</span>)) (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">B</span>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv ' 'se' 't' E '/' | x : T , '/ ' y : U 'in' B ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="dea4596a9f953b0b1b5ed0dd571869e8"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x : T , y : U 'in' B & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">se</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">t</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> -"[ '[hv ' 'se' 't' E '/' | x : T , '/ ' y : U 'in' B '/' & P ] ']'"<br/> - ) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="b8a2bf01275bfb8cd941f3959d622bfa"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x : T 'in' A , y : U ]" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <span class="id" title="var">E</span>) (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> : <span class="id" title="var">T</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#predOfType"><span class="id" title="abbreviation">predOfType</span></a> <span class="id" title="var">U</span>)))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'se' 't' E '/ ' | x : T 'in' A , '/ ' y : U ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="a2d9bb885eac3989797130a8f318c4a6"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x : T 'in' A , y : U & P ]" :=<br/> - (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> (<span class="id" title="var">y</span> : <span class="id" title="var">U</span>) ⇒ <span class="id" title="var">E</span>) (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <span class="id" title="var">A</span>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">_</span> : <span class="id" title="var">T</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <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> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>))<br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> -"[ '[hv ' 'se' 't' E '/' | x : T 'in' A , '/ ' y : U '/' & P ] ']'"<br/> - ) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3c4f47c286c1abd24f4e3930e74b9ede"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x : T , y : U ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">se</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">t</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#predOfType"><span class="id" title="abbreviation">predOfType</span></a> <span class="id" title="var">U</span><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'se' 't' E '/ ' | x : T , '/ ' y : U ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="4112faf42fe59316ff4005ee291adb7e"><span class="id" title="notation">"</span></a>[ 'se' 't' E | x : T , y : U & P ]" :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">se</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">t</span></a> <span class="id" title="var">E</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">:</span></a> <span class="id" title="var">T</span><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">:</span></a> <span class="id" title="var">U</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">in</span></a> <span class="id" title="var">P</span><a class="idref" href="mathcomp.ssreflect.finset.html#6308ce91f23e15d48045c8a55b43b8f5"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0913c49bffa193e6e1e1e7fd77efc6be"><span class="id" title="notation">]</span></a><br/> - (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 0, <span class="id" title="var">E</span>, <span class="id" title="var">x</span>, <span class="id" title="var">y</span> <span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 99, <span class="id" title="var">format</span><br/> - "[ '[hv' 'se' 't' E '/' | x : T , '/ ' y : U '/' & P ] ']'")<br/> - : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FunImage"><span class="id" title="section">FunImage</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="FunImage.aT"><span class="id" title="variable">aT</span></a> <a name="FunImage.aT2"><span class="id" title="variable">aT2</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FunImage.ImsetTheory"><span class="id" title="section">ImsetTheory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FunImage.ImsetTheory.ImsetProp"><span class="id" title="section">ImsetProp</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</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.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a>) (<a name="FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</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.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</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.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imsetP"><span class="id" title="lemma">imsetP</span></a> <span class="id" title="var">D</span> <span class="id" title="var">y</span> : <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> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">x</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#in_mem"><span class="id" title="definition">in_mem</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.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.finset.html#imset"><span class="id" title="abbreviation">imset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Variant</span> <a name="imset2_spec"><span class="id" title="inductive">imset2_spec</span></a> <span class="id" title="var">D1</span> <span class="id" title="var">D2</span> <span class="id" title="var">y</span> : <span class="id" title="keyword">Prop</span> :=<br/> - <a name="Imset2spec"><span class="id" title="constructor">Imset2spec</span></a> <span class="id" title="var">x1</span> <span class="id" title="var">x2</span> <span class="id" title="keyword">of</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#in_mem"><span class="id" title="definition">in_mem</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D1"><span class="id" title="variable">D1</span></a> & <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#in_mem"><span class="id" title="definition">in_mem</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x2"><span class="id" title="variable">x2</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</span></a>) & <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x2"><span class="id" title="variable">x2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2P"><span class="id" title="lemma">imset2P</span></a> <span class="id" title="var">D1</span> <span class="id" title="var">D2</span> <span class="id" title="var">y</span> : <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> (<a class="idref" href="mathcomp.ssreflect.finset.html#imset2_spec"><span class="id" title="inductive">imset2_spec</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.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.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D1"><span class="id" title="variable">D1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="mem_imset"><span class="id" title="lemma">mem_imset</span></a> (<span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#D"><span class="id" title="variable">D</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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset0"><span class="id" title="lemma">imset0</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset_eq0"><span class="id" title="lemma">imset_eq0</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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="imset_set1"><span class="id" title="lemma">imset_set1</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="mem_imset2"><span class="id" title="lemma">mem_imset2</span></a> (<span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">D2</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</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.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) <span class="id" title="var">x</span> <span class="id" title="var">x2</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#D"><span class="id" title="variable">D</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.finset.html#x2"><span class="id" title="variable">x2</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.finset.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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><br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x2"><span class="id" title="variable">x2</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.finset.html#imset2"><span class="id" title="abbreviation">imset2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.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#mem"><span class="id" title="definition">mem</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>) (<span class="id" title="keyword">fun</span> <span class="id" title="var">x1</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#mem"><span class="id" title="definition">mem</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</span></a>)).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="sub_imset_pre"><span class="id" title="lemma">sub_imset_pre</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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="preimsetS"><span class="id" title="lemma">preimsetS</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preimset0"><span class="id" title="lemma">preimset0</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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.finset.html#set0"><span class="id" title="definition">set0</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preimsetT"><span class="id" title="lemma">preimsetT</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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.finset.html#setT"><span class="id" title="abbreviation">setT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preimsetI"><span class="id" title="lemma">preimsetI</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><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.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preimsetU"><span class="id" title="lemma">preimsetU</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preimsetD"><span class="id" title="lemma">preimsetD</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><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.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preimsetC"><span class="id" title="lemma">preimsetC</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><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.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imsetS"><span class="id" title="lemma">imsetS</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset_proper"><span class="id" title="lemma">imset_proper</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preimset_proper"><span class="id" title="lemma">preimset_proper</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#codom"><span class="id" title="definition">codom</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">proper</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f8a5284fd4c86e7670efa54241b49929"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imsetU"><span class="id" title="lemma">imsetU</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imsetU1"><span class="id" title="lemma">imsetU1</span></a> <span class="id" title="var">a</span> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imsetI"><span class="id" title="lemma">imsetI</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">,</span></a> <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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><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.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2Sl"><span class="id" title="lemma">imset2Sl</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2Sr"><span class="id" title="lemma">imset2Sr</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2S"><span class="id" title="lemma">imset2S</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">A2</span> <span class="id" title="var">B2</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A2"><span class="id" title="variable">A2</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B2"><span class="id" title="variable">B2</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.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A2"><span class="id" title="variable">A2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp.f2"><span class="id" title="variable">f2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B2"><span class="id" title="variable">B2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.ImsetProp"><span class="id" title="section">ImsetProp</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">f</span> <span class="id" title="var">g</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</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.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_preimset"><span class="id" title="lemma">eq_preimset</span></a> <span class="id" title="var">f</span> <span class="id" title="var">g</span> <span class="id" title="var">R</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#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#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#g"><span class="id" title="variable">g</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.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#R"><span class="id" title="variable">R</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_imset"><span class="id" title="lemma">eq_imset</span></a> <span class="id" title="var">f</span> <span class="id" title="var">g</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#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#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#g"><span class="id" title="variable">g</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.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_in_imset"><span class="id" title="lemma">eq_in_imset</span></a> <span class="id" title="var">f</span> <span class="id" title="var">g</span> <span class="id" title="var">D</span> : <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.finset.html#D"><span class="id" title="variable">D</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.finset.html#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#876aa133fb3472bffd492f74ff496035"><span class="id" title="notation">=1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#g"><span class="id" title="variable">g</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.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_in_imset2"><span class="id" title="lemma">eq_in_imset2</span></a> (<span class="id" title="var">f</span> <span class="id" title="var">g</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</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.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</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.finset.html#FunImage.ImsetTheory.rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">D2</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#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#c717e24548d7d4d1086535addc681262"><span class="id" title="notation">=2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#g"><span class="id" title="variable">g</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5f76d9959f82823e4253cd67e7dc0e96"><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.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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.finset.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.ImsetTheory"><span class="id" title="section">ImsetTheory</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2_pair"><span class="id" title="lemma">imset2_pair</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">set</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.finset.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.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">,</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#784ffcd4c5fe56ed06653edec4fa118b"><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.finset.html#setX"><span class="id" title="definition">setX</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setXS"><span class="id" title="lemma">setXS</span></a> (<span class="id" title="var">A1</span> <span class="id" title="var">B1</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">A2</span> <span class="id" title="var">B2</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#A1"><span class="id" title="variable">A1</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B1"><span class="id" title="variable">B1</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.finset.html#A2"><span class="id" title="variable">A2</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B2"><span class="id" title="variable">B2</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.finset.html#setX"><span class="id" title="definition">setX</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A1"><span class="id" title="variable">A1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A2"><span class="id" title="variable">A2</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#setX"><span class="id" title="definition">setX</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B1"><span class="id" title="variable">B1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B2"><span class="id" title="variable">B2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImage"><span class="id" title="section">FunImage</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="BigOps"><span class="id" title="section">BigOps</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="BigOps.R"><span class="id" title="variable">R</span></a> : <span class="id" title="keyword">Type</span>) (<a name="BigOps.idx"><span class="id" title="variable">idx</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#R"><span class="id" title="variable">R</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="BigOps.op"><span class="id" title="variable">op</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.law"><span class="id" title="record">Monoid.law</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.idx"><span class="id" title="variable">idx</span></a>) (<a name="BigOps.aop"><span class="id" title="variable">aop</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">Monoid.com_law</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.idx"><span class="id" title="variable">idx</span></a>).<br/> -<span class="id" title="keyword">Variables</span> <a name="BigOps.I"><span class="id" title="variable">I</span></a> <a name="BigOps.J"><span class="id" title="variable">J</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.I"><span class="id" title="variable">I</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">h</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#BigOps.J"><span class="id" title="variable">J</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</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.finset.html#BigOps.I"><span class="id" title="variable">I</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#BigOps.R"><span class="id" title="variable">R</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_set0"><span class="id" title="lemma">big_set0</span></a> <span class="id" title="var">F</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">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.finset.html#BigOps.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.finset.html#BigOps.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.finset.html#set0"><span class="id" title="definition">set0</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#BigOps.idx"><span class="id" title="variable">idx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_set1"><span class="id" title="lemma">big_set1</span></a> <span class="id" title="var">a</span> <span class="id" title="var">F</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">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.finset.html#BigOps.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.finset.html#BigOps.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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a"><span class="id" title="variable">a</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_setID"><span class="id" title="lemma">big_setID</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">F</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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#BigOps.aop"><span class="id" title="variable">aop</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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_setIDcond"><span class="id" title="lemma">big_setIDcond</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">P</span> <span class="id" title="var">F</span> :<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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#BigOps.aop"><span class="id" title="variable">aop</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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>)<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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#160b1f5d5c3e3c6d274924649d717d8d"><span class="id" title="notation">:\:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_setD1"><span class="id" title="lemma">big_setD1</span></a> <span class="id" title="var">a</span> <span class="id" title="var">A</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c91810fcd799fcd960468c603a6be0a6"><span class="id" title="notation">:\</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_setU1"><span class="id" title="lemma">big_setU1</span></a> <span class="id" title="var">a</span> <span class="id" title="var">A</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#a"><span class="id" title="variable">a</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_imset"><span class="id" title="lemma">big_imset</span></a> <span class="id" title="var">h</span> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.I"><span class="id" title="variable">I</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) <span class="id" title="var">G</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.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#b4f176550f5b849a7fbba2ee164934d3"><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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.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.finset.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_imset_cond"><span class="id" title="lemma">big_imset_cond</span></a> <span class="id" title="var">h</span> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.I"><span class="id" title="variable">I</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</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.finset.html#BigOps.J"><span class="id" title="variable">J</span></a>) <span class="id" title="var">G</span> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.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#b4f176550f5b849a7fbba2ee164934d3"><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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#G"><span class="id" title="variable">G</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>)<a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#G"><span class="id" title="variable">G</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="partition_big_imset"><span class="id" title="lemma">partition_big_imset</span></a> <span class="id" title="var">h</span> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.I"><span class="id" title="variable">I</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) <span class="id" title="var">F</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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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.finset.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#BigOps.aop"><span class="id" title="variable">aop</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#BigOps.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">i</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#h"><span class="id" title="variable">h</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#BigOps"><span class="id" title="section">BigOps</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Fun2Set1"><span class="id" title="section">Fun2Set1</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="Fun2Set1.aT1"><span class="id" title="variable">aT1</span></a> <a name="Fun2Set1.aT2"><span class="id" title="variable">aT2</span></a> <a name="Fun2Set1.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="Fun2Set1.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#Fun2Set1.aT1"><span class="id" title="variable">aT1</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.finset.html#Fun2Set1.aT2"><span class="id" title="variable">aT2</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.finset.html#Fun2Set1.rT"><span class="id" title="variable">rT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2_set1l"><span class="id" title="lemma">imset2_set1l</span></a> <span class="id" title="var">x1</span> (<span class="id" title="var">D2</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Fun2Set1.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#Fun2Set1.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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.finset.html#Fun2Set1.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D2"><span class="id" title="variable">D2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2_set1r"><span class="id" title="lemma">imset2_set1r</span></a> <span class="id" title="var">x2</span> (<span class="id" title="var">D1</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Fun2Set1.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#Fun2Set1.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#D1"><span class="id" title="variable">D1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x2"><span class="id" title="variable">x2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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.finset.html#Fun2Set1.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#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x2"><span class="id" title="variable">x2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D1"><span class="id" title="variable">D1</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Fun2Set1"><span class="id" title="section">Fun2Set1</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="CardFunImage"><span class="id" title="section">CardFunImage</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="CardFunImage.aT"><span class="id" title="variable">aT</span></a> <a name="CardFunImage.aT2"><span class="id" title="variable">aT2</span></a> <a name="CardFunImage.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Variables</span> (<a name="CardFunImage.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.aT"><span class="id" title="variable">aT</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.finset.html#CardFunImage.rT"><span class="id" title="variable">rT</span></a>) (<a name="CardFunImage.g"><span class="id" title="variable">g</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.rT"><span class="id" title="variable">rT</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.finset.html#CardFunImage.aT"><span class="id" title="variable">aT</span></a>) (<a name="CardFunImage.f2"><span class="id" title="variable">f2</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.aT"><span class="id" title="variable">aT</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.finset.html#CardFunImage.aT2"><span class="id" title="variable">aT2</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.finset.html#CardFunImage.rT"><span class="id" title="variable">rT</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="CardFunImage.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<a name="CardFunImage.D2"><span class="id" title="variable">D2</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.aT"><span class="id" title="variable">aT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset_card"><span class="id" title="lemma">imset_card</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#image"><span class="id" title="abbreviation">image</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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="leq_imset_card"><span class="id" title="lemma">leq_imset_card</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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#cb53cf0ee22c036a03b4a9281c68b5a3"><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.finset.html#CardFunImage.D"><span class="id" title="variable">D</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="card_in_imset"><span class="id" title="lemma">card_in_imset</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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="card_imset"><span class="id" title="lemma">card_imset</span></a> : <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.finset.html#CardFunImage.f"><span class="id" title="variable">f</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="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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="imset_injP"><span class="id" title="lemma">imset_injP</span></a> : <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> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><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.finset.html#CardFunImage.D"><span class="id" title="variable">D</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="can2_in_imset_pre"><span class="id" title="lemma">can2_in_imset_pre</span></a> :<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.finset.html#CardFunImage.D"><span class="id" title="variable">D</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.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.g"><span class="id" title="variable">g</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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#0464b66a9c149dd6cf0212db00d53c7f"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#0464b66a9c149dd6cf0212db00d53c7f"><span class="id" title="notation">on</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#0464b66a9c149dd6cf0212db00d53c7f"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.g"><span class="id" title="variable">g</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#0464b66a9c149dd6cf0212db00d53c7f"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#0464b66a9c149dd6cf0212db00d53c7f"><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.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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.finset.html#CardFunImage.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="can2_imset_pre"><span class="id" title="lemma">can2_imset_pre</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.g"><span class="id" title="variable">g</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#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.f"><span class="id" title="variable">f</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.finset.html#CardFunImage.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</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.finset.html#CardFunImage.g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage.D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#CardFunImage"><span class="id" title="section">CardFunImage</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="on_card_preimset"><span class="id" title="lemma">on_card_preimset</span></a> (<span class="id" title="var">aT</span> <span class="id" title="var">rT</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.finset.html#aT"><span class="id" title="variable">aT</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.finset.html#rT"><span class="id" title="variable">rT</span></a>) (<span class="id" title="var">R</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#rT"><span class="id" title="variable">rT</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :<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="mathcomp.ssreflect.finset.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#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.finset.html#f"><span class="id" title="variable">f</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#R"><span class="id" title="variable">R</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#R"><span class="id" title="variable">R</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="can_imset_pre"><span class="id" title="lemma">can_imset_pre</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>) <span class="id" title="var">f</span> <span class="id" title="var">g</span> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#g"><span class="id" title="variable">g</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.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b8b2ebc8e1a8b9aa935c0702efb5dccf"><span class="id" title="notation">:></span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset_id"><span class="id" title="lemma">imset_id</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>) (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) : <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="card_preimset"><span class="id" title="lemma">card_preimset</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>) (<span class="id" title="var">f</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<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.finset.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.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="mathcomp.ssreflect.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#a26e64199ff8828f9b3d592a35c487af"><span class="id" title="notation">@^-1:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="card_powerset"><span class="id" title="lemma">card_powerset</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>) (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><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.finset.html#powerset"><span class="id" title="definition">powerset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> 2 <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.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="FunImageComp"><span class="id" title="section">FunImageComp</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="FunImageComp.T"><span class="id" title="variable">T</span></a> <a name="FunImageComp.T'"><span class="id" title="variable">T'</span></a> <a name="FunImageComp.U"><span class="id" title="variable">U</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset_comp"><span class="id" title="lemma">imset_comp</span></a> (<span class="id" title="var">f</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImageComp.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.finset.html#FunImageComp.U"><span class="id" title="variable">U</span></a>) (<span class="id" title="var">g</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#FunImageComp.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.finset.html#FunImageComp.T'"><span class="id" title="variable">T'</span></a>) (<span class="id" title="var">H</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImageComp.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#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#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.finset.html#g"><span class="id" title="variable">g</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#g"><span class="id" title="variable">g</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#H"><span class="id" title="variable">H</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#FunImageComp"><span class="id" title="section">FunImageComp</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">"</span></a>\bigcup_ ( 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.finset.html#setU"><span class="id" 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title="var">F</span>%<span class="id" title="var">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="457cf1b9753bd632a5ab6a6f47fd6ac7"><span class="id" title="notation">"</span></a>\bigcup_ ( 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.finset.html#setU"><span class="id" title="definition">setU</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" 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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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">"</span></a>\bigcup_ ( 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.finset.html#setU"><span class="id" title="definition">setU</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</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> <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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Notation</span> <a name="0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</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.finset.html#setT"><span class="id" title="abbreviation">setT</span></a><a class="idref" href="mathcomp.ssreflect.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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="8cec6a11d2b62c9271c798594f29aa6d"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#93a42d9430a115f2544a09cba4cf05ca"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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> <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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="ff7e82ab4c7315510371b5620aba09dc"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#61699f7bcd958ceac6b63f7e240f7ee7"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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><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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="1ca21f047ead227ec4d3839d61337aff"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#a0f72dd08c3295710348031e7df784a3"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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><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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#1871917561e26284874cb982a8cc32df"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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> 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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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d9e61c197d846298f3e26b588e67e5ec"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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><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">SET</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>): <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="f5e9801753a22f2d2c2c6a052563baf1"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0a668c1f377e113a6f68dd824f1c2031"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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">(</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">SET</span>) (<span class="id" title="var">only</span> <span class="id" title="var">parsing</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="27fb056d0ab27107566bb9722b69ede4"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#0b83d32979b1fdd5833879356bbfd57b"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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> <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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="14fdde2e94f7dc27f42b5df80a2d3520"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#afef6bddeda988bbc365e556241d5732"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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> <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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="2177fb8f135b8655f721a7c9df5fc9eb"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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">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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> -<span class="id" title="keyword">Notation</span> <a name="17be462b372c78f64262e282e98f2452"><span class="id" title="notation">"</span></a>\bigcap_ ( 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.finset.html#setI"><span class="id" title="definition">setI</span></a> <span class="id" title="var">_</span><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">/</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setT"><span class="id" title="abbreviation">setT</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> <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">SET</span>) : <span class="id" title="var">set_scope</span>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="BigSetOps"><span class="id" title="section">BigSetOps</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="BigSetOps.T"><span class="id" title="variable">T</span></a> <a name="BigSetOps.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>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">U</span> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigSetOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</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.finset.html#BigSetOps.I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigSetOps.I"><span class="id" title="variable">I</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#BigSetOps.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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigSetOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -</div> - -<div class="doc"> - It is very hard to use this lemma, because the unification fails to - defer the F j pattern (even though it's a Miller pattern!). -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="bigcup_sup"><span class="id" title="lemma">bigcup_sup</span></a> <span class="id" title="var">j</span> <span class="id" title="var">P</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcup_max"><span class="id" title="lemma">bigcup_max</span></a> <span class="id" title="var">j</span> <span class="id" title="var">U</span> <span class="id" title="var">P</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcupP"><span class="id" title="lemma">bigcupP</span></a> <span class="id" title="var">x</span> <span class="id" title="var">P</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> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">exists2</span></a> <span class="id" title="var">i</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#3df228c109f14f0423b4fccc967ee1ac"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcupsP"><span class="id" title="lemma">bigcupsP</span></a> <span class="id" title="var">U</span> <span class="id" title="var">P</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.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#U"><span class="id" title="variable">U</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#U"><span class="id" title="variable">U</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcup_disjoint"><span class="id" title="lemma">bigcup_disjoint</span></a> <span class="id" title="var">U</span> <span class="id" title="var">P</span> <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.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.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.finset.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</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> <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#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.finset.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#30cfba5ac0056b0b6e6dae61e139d94a"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcup_setU"><span class="id" title="lemma">bigcup_setU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcup_seq"><span class="id" title="lemma">bigcup_seq</span></a> <span class="id" title="var">r</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#6831c3e6cae5ef17f89a485d9445f0cb"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6831c3e6cae5ef17f89a485d9445f0cb"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6831c3e6cae5ef17f89a485d9445f0cb"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#6831c3e6cae5ef17f89a485d9445f0cb"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#6831c3e6cae5ef17f89a485d9445f0cb"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - Unlike its setU counterpart, this lemma is useable. -</div> -<div class="code"> -<span class="id" title="keyword">Lemma</span> <a name="bigcap_inf"><span class="id" title="lemma">bigcap_inf</span></a> <span class="id" title="var">j</span> <span class="id" title="var">P</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcap_min"><span class="id" title="lemma">bigcap_min</span></a> <span class="id" title="var">j</span> <span class="id" title="var">U</span> <span class="id" title="var">P</span> <span class="id" title="var">F</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#U"><span class="id" title="variable">U</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.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#U"><span class="id" title="variable">U</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcapsP"><span class="id" title="lemma">bigcapsP</span></a> <span class="id" title="var">U</span> <span class="id" title="var">P</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.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#U"><span class="id" title="variable">U</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcapP"><span class="id" title="lemma">bigcapP</span></a> <span class="id" title="var">x</span> <span class="id" title="var">P</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.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ed4f70cb75d6b4771a0be60d14037c7b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setC_bigcup"><span class="id" title="lemma">setC_bigcup</span></a> <span class="id" title="var">J</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.finset.html#J"><span class="id" title="variable">J</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigSetOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><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.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setC_bigcap"><span class="id" title="lemma">setC_bigcap</span></a> <span class="id" title="var">J</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.finset.html#J"><span class="id" title="variable">J</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#BigSetOps.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#0e81c215a8a995136d6989d77fd3e46b"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><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.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">(</span></a><span class="id" title="var">j</span> <a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b4337583ce0da9b8360e25d42b6b5ba5"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcap_setU"><span class="id" title="lemma">bigcap_setU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <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#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="bigcap_seq"><span class="id" title="lemma">bigcap_seq</span></a> <span class="id" title="var">r</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#8cec6a11d2b62c9271c798594f29aa6d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#8cec6a11d2b62c9271c798594f29aa6d"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#8cec6a11d2b62c9271c798594f29aa6d"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#8cec6a11d2b62c9271c798594f29aa6d"><span class="id" title="notation"><-</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#8cec6a11d2b62c9271c798594f29aa6d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">bigcap_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#r"><span class="id" title="variable">r</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#17be462b372c78f64262e282e98f2452"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#BigSetOps"><span class="id" title="section">BigSetOps</span></a>.<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ImsetCurry"><span class="id" title="section">ImsetCurry</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ImsetCurry.aT1"><span class="id" title="variable">aT1</span></a> <a name="ImsetCurry.aT2"><span class="id" title="variable">aT2</span></a> <a name="ImsetCurry.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>) (<a name="ImsetCurry.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#aT1"><span class="id" title="variable">aT1</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.finset.html#aT2"><span class="id" title="variable">aT2</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.finset.html#rT"><span class="id" title="variable">rT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="ImsetCurry.Curry"><span class="id" title="section">Curry</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="ImsetCurry.Curry.A1"><span class="id" title="variable">A1</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="ImsetCurry.Curry.A2"><span class="id" title="variable">A2</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Variables</span> (<a name="ImsetCurry.Curry.D1"><span class="id" title="variable">D1</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>) (<a name="ImsetCurry.Curry.D2"><span class="id" title="variable">D2</span></a> : <a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">pred</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.ssrbool.html#64f8873130736b599801d4930af00e74"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="curry_imset2X"><span class="id" title="lemma">curry_imset2X</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.A1"><span class="id" title="variable">A1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.A2"><span class="id" title="variable">A2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#prod_curry"><span class="id" title="definition">prod_curry</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#setX"><span class="id" title="definition">setX</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.A1"><span class="id" title="variable">A1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.A2"><span class="id" title="variable">A2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="curry_imset2l"><span class="id" title="lemma">curry_imset2l</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D2"><span class="id" title="variable">D2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">x1</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x1"><span class="id" title="variable">x1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D2"><span class="id" title="variable">D2</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="curry_imset2r"><span class="id" title="lemma">curry_imset2r</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D1"><span class="id" title="variable">D1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D2"><span class="id" title="variable">D2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">x2</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D2"><span class="id" title="variable">D2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.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#d89396f990d6b54d736cfe259e498cf4"><span class="id" title="notation">^~</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x2"><span class="id" title="variable">x2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry.D1"><span class="id" title="variable">D1</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.Curry"><span class="id" title="section">Curry</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2Ul"><span class="id" title="lemma">imset2Ul</span></a> (<span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="imset2Ur"><span class="id" title="lemma">imset2Ur</span></a> (<span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT1"><span class="id" title="variable">aT1</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.aT2"><span class="id" title="variable">aT2</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><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.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">@2:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#139da7153badf64948e6ab411b5a9cdd"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#ImsetCurry"><span class="id" title="section">ImsetCurry</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Partitions"><span class="id" title="section">Partitions</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> <a name="Partitions.T"><span class="id" title="variable">T</span></a> <a name="Partitions.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>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">x</span> <span class="id" title="var">y</span> <span class="id" title="var">z</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">D</span> <span class="id" title="var">X</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<span class="id" title="var">P</span> <span class="id" title="var">Q</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}}</span></a>).<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> (<span class="id" title="var">J</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.finset.html#Partitions.I"><span class="id" title="variable">I</span></a>) (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="cover"><span class="id" title="definition">cover</span></a> <span class="id" title="var">P</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="pblock"><span class="id" title="definition">pblock</span></a> <span class="id" title="var">P</span> <span class="id" title="var">x</span> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#odflt"><span class="id" title="abbreviation">odflt</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> (<a class="idref" href="mathcomp.ssreflect.fintype.html#pick"><span class="id" title="definition">pick</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">[</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">pred</span></a> <span class="id" title="var">B</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.ssrbool.html#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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#9485b92620b46b20355750aaf9f28020"><span class="id" title="notation">]</span></a>).<br/> -<span class="id" title="keyword">Definition</span> <a name="trivIset"><span class="id" title="definition">trivIset</span></a> <span class="id" title="var">P</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">B</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><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.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><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.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="partition"><span class="id" title="definition">partition</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">[&&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="is_transversal"><span class="id" title="definition">is_transversal</span></a> <span class="id" title="var">X</span> <span class="id" title="var">P</span> <span class="id" title="var">D</span> :=<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">[&&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#9b40a7420e06ba2a775d87b43bd1c69f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#9b40a7420e06ba2a775d87b43bd1c69f"><span class="id" title="notation">∀</span></a> <span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#9b40a7420e06ba2a775d87b43bd1c69f"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#f3be25edeb0349b0a76405eded9d0b98"><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.finset.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1<a class="idref" href="mathcomp.ssreflect.fintype.html#9b40a7420e06ba2a775d87b43bd1c69f"><span class="id" title="notation">]</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#5a7d806905be2a0d04047156433535f1"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="transversal"><span class="id" title="definition">transversal</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">set</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#odflt"><span class="id" title="abbreviation">odflt</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">pick</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">]</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="transversal_repr"><span class="id" title="definition">transversal_repr</span></a> <span class="id" title="var">x0</span> <span class="id" title="var">X</span> <span class="id" title="var">B</span> := <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#odflt"><span class="id" title="abbreviation">odflt</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">pick</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#c37d1b05b70882746ce17952ea00c535"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="leq_card_setU"><span class="id" title="lemma">leq_card_setU</span></a> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#3bfdad100117c55128c8f4e205b0209b"><span class="id" title="notation">:|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#22d09a36997010daec8f30c044c9e5d4"><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.finset.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#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="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#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#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.finset.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.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="leq_card_cover"><span class="id" title="lemma">leq_card_cover</span></a> <span class="id" title="var">P</span> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</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#22d09a36997010daec8f30c044c9e5d4"><span class="id" title="notation">≤</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">A</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><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.finset.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#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.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="trivIsetP"><span class="id" title="lemma">trivIsetP</span></a> <span class="id" title="var">P</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> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span>, <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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#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.finset.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.finset.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.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="trivIsetS"><span class="id" title="lemma">trivIsetS</span></a> <span class="id" title="var">P</span> <span class="id" title="var">Q</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Q"><span class="id" title="variable">Q</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.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Q"><span class="id" title="variable">Q</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.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="trivIsetI"><span class="id" title="lemma">trivIsetI</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#7ed77f64965385480255328de15d774c"><span class="id" title="notation">::&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cover_setI"><span class="id" title="lemma">cover_setI</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#7ed77f64965385480255328de15d774c"><span class="id" title="notation">::&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="mem_pblock"><span class="id" title="lemma">mem_pblock</span></a> <span class="id" title="var">P</span> <span class="id" title="var">x</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.finset.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.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.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pblock_mem"><span class="id" title="lemma">pblock_mem</span></a> <span class="id" title="var">P</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="def_pblock"><span class="id" title="lemma">def_pblock</span></a> <span class="id" title="var">P</span> <span class="id" title="var">B</span> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="same_pblock"><span class="id" title="lemma">same_pblock</span></a> <span class="id" title="var">P</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="eq_pblock"><span class="id" title="lemma">eq_pblock</span></a> <span class="id" title="var">P</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.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.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="trivIsetU1"><span class="id" title="lemma">trivIsetU1</span></a> <span class="id" title="var">A</span> <span class="id" title="var">P</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.finset.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.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">B</span>, <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.finset.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.finset.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.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.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#c07c66784631827a3968dee93baba0d0"><span class="id" title="notation">|:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cover_imset"><span class="id" title="lemma">cover_imset</span></a> <span class="id" title="var">J</span> <span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">bigcup_</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">(</span></a><span class="id" title="var">i</span> <a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#J"><span class="id" title="variable">J</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#3807eb776e98d53eeae3c7eceb88122d"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="trivIimset"><span class="id" title="lemma">trivIimset</span></a> <span class="id" title="var">J</span> <span class="id" title="var">F</span> (<span class="id" title="var">P</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b4f176550f5b849a7fbba2ee164934d3"><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.finset.html#j"><span class="id" title="variable">j</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#c385a484ee9d1b4e0615924561a9b75e"><span class="id" title="notation">!=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</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.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><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.finset.html#set0"><span class="id" title="definition">set0</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.html#F"><span class="id" title="variable">F</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="cover_partition"><span class="id" title="lemma">cover_partition</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="card_partition"><span class="id" title="lemma">card_partition</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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> <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">A</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#cd344b81961f1f1b59f55b98384ad290"><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.finset.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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="card_uniform_partition"><span class="id" title="lemma">card_uniform_partition</span></a> <span class="id" title="var">n</span> <span class="id" title="var">P</span> <span class="id" title="var">D</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.finset.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.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <span class="id" title="keyword">∀</span> <span class="id" title="var">A</span>, <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.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> <a class="idref" href="mathcomp.ssreflect.finset.html#n"><span class="id" title="variable">n</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.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</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.finset.html#n"><span class="id" title="variable">n</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Partitions.BigOps"><span class="id" title="section">BigOps</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Partitions.BigOps.R"><span class="id" title="variable">R</span></a> : <span class="id" title="keyword">Type</span>) (<a name="Partitions.BigOps.idx"><span class="id" title="variable">idx</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#R"><span class="id" title="variable">R</span></a>) (<a name="Partitions.BigOps.op"><span class="id" title="variable">op</span></a> : <a class="idref" href="mathcomp.ssreflect.bigop.html#Monoid.com_law"><span class="id" title="record">Monoid.com_law</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#idx"><span class="id" title="variable">idx</span></a>).<br/> -<span class="id" title="keyword">Let</span> <a name="Partitions.BigOps.rhs_cond"><span class="id" title="variable">rhs_cond</span></a> <span class="id" title="var">P</span> <span class="id" title="var">K</span> <span class="id" title="var">E</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">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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">A</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</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#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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>.<br/> -<span class="id" title="keyword">Let</span> <a name="Partitions.BigOps.rhs"><span class="id" title="variable">rhs</span></a> <span class="id" title="var">P</span> <span class="id" title="var">E</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">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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">A</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</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">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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_trivIset_cond"><span class="id" title="lemma">big_trivIset_cond</span></a> <span class="id" title="var">P</span> (<span class="id" title="var">K</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.finset.html#Partitions.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">E</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.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.finset.html#Partitions.BigOps.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#Partitions.BigOps.rhs_cond"><span class="id" title="variable">rhs_cond</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="big_trivIset"><span class="id" title="lemma">big_trivIset</span></a> <span class="id" title="var">P</span> (<span class="id" title="var">E</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.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.finset.html#Partitions.BigOps.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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> <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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#Partitions.BigOps.rhs"><span class="id" title="variable">rhs</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set_partition_big_cond"><span class="id" title="lemma">set_partition_big_cond</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> (<span class="id" title="var">K</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.finset.html#Partitions.T"><span class="id" title="variable">T</span></a>) (<span class="id" title="var">E</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.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.finset.html#Partitions.BigOps.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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#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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d82d692725683c4eeb1ed4ba22855f30"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#Partitions.BigOps.rhs_cond"><span class="id" title="variable">rhs_cond</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#K"><span class="id" title="variable">K</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="set_partition_big"><span class="id" title="lemma">set_partition_big</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> (<span class="id" title="var">E</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.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.finset.html#Partitions.BigOps.R"><span class="id" title="variable">R</span></a>) :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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#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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#Partitions.BigOps.rhs"><span class="id" title="variable">rhs</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="partition_disjoint_bigcup"><span class="id" title="lemma">partition_disjoint_bigcup</span></a> (<span class="id" title="var">F</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.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.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">E</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.finset.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.finset.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#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.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#1c170b7d9dd618ec64d5610e390a3afe"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#j"><span class="id" title="variable">j</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> <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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#31d99c97f818421e6bff286f558a013d"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#31d99c97f818421e6bff286f558a013d"><span class="id" title="notation">bigcup_i</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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><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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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#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.finset.html#Partitions.BigOps.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.finset.html#Partitions.BigOps.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">x</span> <a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#F"><span class="id" title="variable">F</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#i"><span class="id" title="variable">i</span></a><a class="idref" href="mathcomp.ssreflect.bigop.html#d37140b0b5d9683da109df6bc7f32772"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#E"><span class="id" title="variable">E</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.BigOps"><span class="id" title="section">BigOps</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Partitions.Equivalence"><span class="id" title="section">Equivalence</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Partitions.Equivalence.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#rel"><span class="id" title="definition">rel</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a>) (<a name="Partitions.Equivalence.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="Partitions.Equivalence.Px"><span class="id" title="variable">Px</span></a> <span class="id" title="var">x</span> := <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">set</span></a> <span class="id" title="var">y</span> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.D"><span class="id" title="variable">D</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#91816551bcea1b6f359ecf76f3595e38"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Definition</span> <a name="equivalence_partition"><span class="id" title="definition">equivalence_partition</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.Px"><span class="id" title="variable">Px</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">|</span></a> <span class="id" title="var">x</span> <a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.D"><span class="id" title="variable">D</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#1e993786ab46c6f2c0d488e43f629b71"><span class="id" title="notation">]</span></a>.<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Partitions.Equivalence.eqiR"><span class="id" title="variable">eqiR</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#equivalence_rel"><span class="id" title="definition">equivalence_rel</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.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#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="Partitions.Equivalence.Pxx"><span class="id" title="variable">Pxx</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#Partitions.Equivalence.D"><span class="id" title="variable">D</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.finset.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.finset.html#Partitions.Equivalence.Px"><span class="id" title="variable">Px</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>.<br/> - <span class="id" title="keyword">Let</span> <a name="Partitions.Equivalence.PPx"><span class="id" title="variable">PPx</span></a> <span class="id" title="var">x</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#Partitions.Equivalence.D"><span class="id" title="variable">D</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.finset.html#Partitions.Equivalence.Px"><span class="id" title="variable">Px</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#P"><span class="id" title="abbreviation">P</span></a> := <span class="id" title="keyword">fun</span> <span class="id" title="var">Dx</span> ⇒ <a class="idref" href="mathcomp.ssreflect.finset.html#mem_imset"><span class="id" title="lemma">mem_imset</span></a> <span class="id" title="var">_</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Dx"><span class="id" title="variable">Dx</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="equivalence_partitionP"><span class="id" title="lemma">equivalence_partitionP</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="abbreviation">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pblock_equivalence_partition"><span class="id" title="lemma">pblock_equivalence_partition</span></a> :<br/> - <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence.D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</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="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.finset.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.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="abbreviation">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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="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.finset.html#Partitions.Equivalence.R"><span class="id" title="variable">R</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Equivalence"><span class="id" title="section">Equivalence</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pblock_equivalence"><span class="id" title="lemma">pblock_equivalence</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">&</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">&,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#equivalence_rel"><span class="id" title="definition">equivalence_rel</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <a class="idref" href="mathcomp.ssreflect.finset.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.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#41940d7b27ea6f4cfc62b9919ed9d131"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="equivalence_partition_pblock"><span class="id" title="lemma">equivalence_partition_pblock</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#equivalence_partition"><span class="id" title="definition">equivalence_partition</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <a class="idref" href="mathcomp.ssreflect.finset.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.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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Partitions.Preim"><span class="id" title="section">Preim</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Partitions.Preim.rT"><span class="id" title="variable">rT</span></a> : <a class="idref" href="mathcomp.ssreflect.eqtype.html#Equality.Exports.eqType"><span class="id" title="abbreviation">eqType</span></a>) (<a name="Partitions.Preim.f"><span class="id" title="variable">f</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.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.finset.html#rT"><span class="id" title="variable">rT</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="preim_partition"><span class="id" title="definition">preim_partition</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#equivalence_partition"><span class="id" title="definition">equivalence_partition</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span> ⇒ <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Preim.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Preim.f"><span class="id" title="variable">f</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#y"><span class="id" title="variable">y</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preim_partitionP"><span class="id" title="lemma">preim_partitionP</span></a> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#preim_partition"><span class="id" title="definition">preim_partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Preim"><span class="id" title="section">Preim</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="preim_partition_pblock"><span class="id" title="lemma">preim_partition_pblock</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#preim_partition"><span class="id" title="definition">preim_partition</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="transversalP"><span class="id" title="lemma">transversalP</span></a> <span class="id" title="var">P</span> <span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#is_transversal"><span class="id" title="definition">is_transversal</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#transversal"><span class="id" title="definition">transversal</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Section</span> <a name="Partitions.Transversals"><span class="id" title="section">Transversals</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variables</span> (<a name="Partitions.Transversals.X"><span class="id" title="variable">X</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) (<a name="Partitions.Transversals.P"><span class="id" title="variable">P</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}}</span></a>) (<a name="Partitions.Transversals.D"><span class="id" title="variable">D</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>).<br/> -<span class="id" title="keyword">Hypothesis</span> <a name="Partitions.Transversals.trPX"><span class="id" title="variable">trPX</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#is_transversal"><span class="id" title="definition">is_transversal</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.D"><span class="id" title="variable">D</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="transversal_sub"><span class="id" title="lemma">transversal_sub</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.D"><span class="id" title="variable">D</span></a>. <br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="Partitions.Transversals.tiP"><span class="id" title="variable">tiP</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#trivIset"><span class="id" title="definition">trivIset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</span></a>. <br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="Partitions.Transversals.sXP"><span class="id" title="variable">sXP</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.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#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">≤</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#ca592708f529c7c7ee5f3dbd6cf93463"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Let</span> <a name="Partitions.Transversals.trX"><span class="id" title="variable">trX</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.ssr.ssrbool.html#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</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> <span class="id" title="keyword">∀</span> <span class="id" title="var">B</span>, <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> 1<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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="setI_transversal_pblock"><span class="id" title="lemma">setI_transversal_pblock</span></a> <span class="id" title="var">x0</span> <span class="id" title="var">B</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#Partitions.Transversals.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> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#b9596739b058766532fc6517a36fef9f"><span class="id" title="notation">:&:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#transversal_repr"><span class="id" title="definition">transversal_repr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#f5e197738ea7c8e266850f6045418c3f"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="repr_mem_pblock"><span class="id" title="lemma">repr_mem_pblock</span></a> <span class="id" title="var">x0</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#Partitions.Transversals.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> <a class="idref" href="mathcomp.ssreflect.finset.html#transversal_repr"><span class="id" title="definition">transversal_repr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#B"><span class="id" title="variable">B</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="repr_mem_transversal"><span class="id" title="lemma">repr_mem_transversal</span></a> <span class="id" title="var">x0</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#Partitions.Transversals.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> <a class="idref" href="mathcomp.ssreflect.finset.html#transversal_repr"><span class="id" title="definition">transversal_repr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="transversal_reprK"><span class="id" title="lemma">transversal_reprK</span></a> <span class="id" title="var">x0</span> : <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.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</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.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#transversal_repr"><span class="id" title="definition">transversal_repr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</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>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pblockK"><span class="id" title="lemma">pblockK</span></a> <span class="id" title="var">x0</span> : <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.finset.html#Partitions.Transversals.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#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrfun.html#cancel"><span class="id" title="definition">cancel</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#transversal_repr"><span class="id" title="definition">transversal_repr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.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#8c08d4203604dbed63e7afa9b689d858"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pblock_inj"><span class="id" title="lemma">pblock_inj</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.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#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</span></a>)<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="pblock_transversal"><span class="id" title="lemma">pblock_transversal</span></a> : <a class="idref" href="mathcomp.ssreflect.finset.html#pblock"><span class="id" title="definition">pblock</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.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.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="card_transversal"><span class="id" title="lemma">card_transversal</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</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> <a class="idref" href="mathcomp.ssreflect.fintype.html#234f50e13366f794cd6877cf832a5935"><span class="id" title="notation">#|</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.P"><span class="id" title="variable">P</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="im_transversal_repr"><span class="id" title="lemma">im_transversal_repr</span></a> <span class="id" title="var">x0</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#transversal_repr"><span class="id" title="definition">transversal_repr</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#x0"><span class="id" title="variable">x0</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.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#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals.X"><span class="id" title="variable">X</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions.Transversals"><span class="id" title="section">Transversals</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#Partitions"><span class="id" title="section">Partitions</span></a>.<br/> - -<br/> - -<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="partition_partition"><span class="id" title="lemma">partition_partition</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>) (<span class="id" title="var">D</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>) <span class="id" title="var">P</span> <span class="id" title="var">Q</span> :<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</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.finset.html#partition"><span class="id" title="definition">partition</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#partition"><span class="id" title="definition">partition</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#cover"><span class="id" title="definition">cover</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#de2c3fcab69008133cce8f8fc06f2b4b"><span class="id" title="notation">@:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Q"><span class="id" title="variable">Q</span></a>) <a class="idref" href="mathcomp.ssreflect.finset.html#D"><span class="id" title="variable">D</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">in</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#Q"><span class="id" title="variable">Q</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">&,</span></a> <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.finset.html#cover"><span class="id" title="definition">cover</span></a><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssrbool.html#b4f176550f5b849a7fbba2ee164934d3"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -</div> - -<div class="doc"> - -<div class="paragraph"> </div> - - Maximum and minimun (sub)set with respect to a given pred - -</div> -<div class="code"> - -<br/> -<span class="id" title="keyword">Section</span> <a name="MaxSetMinSet"><span class="id" title="section">MaxSetMinSet</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Variable</span> <a name="MaxSetMinSet.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="mathcomp.ssreflect.fintype.html#Finite.Exports.finType"><span class="id" title="abbreviation">finType</span></a>.<br/> -<span class="id" title="keyword">Notation</span> <a name="sT"><span class="id" title="abbreviation">sT</span></a> := <a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">{</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">set</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#MaxSetMinSet.T"><span class="id" title="variable">T</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#d8708f36d374a98f4d683c7593d1ea6a"><span class="id" title="notation">}</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#sT"><span class="id" title="abbreviation">sT</span></a>.<br/> -<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</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.finset.html#sT"><span class="id" title="abbreviation">sT</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Definition</span> <a name="minset"><span class="id" title="definition">minset</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> := <a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">[</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">∀</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">(</span></a><span class="id" title="var">B</span> <a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#sT"><span class="id" title="abbreviation">sT</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><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.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a><a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">)</span></a> <a class="idref" href="mathcomp.ssreflect.eqtype.html#df45e8c2e8370fd4f0f7c4fdaf208180"><span class="id" title="notation">==</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#b14c43cd248537980c3a1a815ab087df"><span class="id" title="notation">]</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="minset_eq"><span class="id" title="lemma">minset_eq</span></a> <span class="id" title="var">P1</span> <span class="id" title="var">P2</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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="mathcomp.ssreflect.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="minsetP"><span class="id" title="lemma">minsetP</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</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> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">B</span>, <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">)</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="minsetp"><span class="id" title="lemma">minsetp</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="minsetinf"><span class="id" title="lemma">minsetinf</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="ex_minset"><span class="id" title="lemma">ex_minset</span></a> <span class="id" title="var">P</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><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">A</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">{</span></a><span class="id" title="var">A</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="minset_exists"><span class="id" title="lemma">minset_exists</span></a> <span class="id" title="var">P</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.Specif.html#c0bbd202248f4def7aaf0c316cf2c29e"><span class="id" title="notation">{</span></a><span class="id" title="var">A</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.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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/> -</div> - -<div class="doc"> - The 'locked_with' allows Coq to find the value of P by unification. -</div> -<div class="code"> -<span class="id" title="keyword">Fact</span> <a name="maxset_key"><span class="id" title="lemma">maxset_key</span></a> : <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Datatypes.html#unit"><span class="id" title="inductive">unit</span></a>. <br/> -<span class="id" title="keyword">Definition</span> <a name="maxset"><span class="id" title="definition">maxset</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> :=<br/> - <a class="idref" href="mathcomp.ssreflect.finset.html#minset"><span class="id" title="definition">minset</span></a> (<span class="id" title="keyword">fun</span> <span class="id" title="var">B</span> ⇒ <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.ssr.ssreflect.html#locked_with"><span class="id" title="definition">locked_with</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#maxset_key"><span class="id" title="lemma">maxset_key</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</span></a>)) (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="maxset_eq"><span class="id" title="lemma">maxset_eq</span></a> <span class="id" title="var">P1</span> <span class="id" title="var">P2</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.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.finset.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="mathcomp.ssreflect.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P1"><span class="id" title="variable">P1</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P2"><span class="id" title="variable">P2</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="maxminset"><span class="id" title="lemma">maxminset</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#minset"><span class="id" title="definition">minset</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">B</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.finset.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">]</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="minmaxset"><span class="id" title="lemma">minmaxset</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#minset"><span class="id" title="definition">minset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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.finset.html#maxset"><span class="id" title="definition">maxset</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">B</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.finset.html#P"><span class="id" title="variable">P</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#27dabc72ea2c2c768f2db80a79f42524"><span class="id" title="notation">]</span></a> (<a class="idref" href="mathcomp.ssreflect.finset.html#b5b2e79e9aa4d1421d843544332af584"><span class="id" title="notation">~:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="maxsetP"><span class="id" title="lemma">maxsetP</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</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> (<a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">(</span></a><a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">∧</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">(</span></a><span class="id" title="keyword">∀</span> <span class="id" title="var">B</span>, <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</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.finset.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#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">)</span></a>) (<a class="idref" href="mathcomp.ssreflect.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>).<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="maxsetp"><span class="id" title="lemma">maxsetp</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="maxsetsup"><span class="id" title="lemma">maxsetsup</span></a> <span class="id" title="var">P</span> <span class="id" title="var">A</span> <span class="id" title="var">B</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#1c93e43e07fbeaeb6a625cb6614beb5d"><span class="id" title="notation">→</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#B"><span class="id" title="variable">B</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.finset.html#B"><span class="id" title="variable">B</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.finset.html#A"><span class="id" title="variable">A</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="ex_maxset"><span class="id" title="lemma">ex_maxset</span></a> <span class="id" title="var">P</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><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">∃</span></a> <span class="id" title="var">A</span><a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span class="id" title="notation">,</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#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="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">{</span></a><span class="id" title="var">A</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#bc4528e836ab0e91ea7e942fb09e898f"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">Lemma</span> <a name="maxset_exists"><span class="id" title="lemma">maxset_exists</span></a> <span class="id" title="var">P</span> <span class="id" title="var">C</span> : <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</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.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">{</span></a><span class="id" title="var">A</span> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">:</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#sT"><span class="id" title="abbreviation">sT</span></a> <a class="idref" href="http://coq.inria.fr/distrib/V8.9.0/stdlib//Coq.Init.Specif.html#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">|</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#maxset"><span class="id" title="definition">maxset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#P"><span class="id" title="variable">P</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">&</span></a> <a class="idref" href="mathcomp.ssreflect.finset.html#C"><span class="id" title="variable">C</span></a> <a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">\</span></a><a class="idref" href="mathcomp.ssreflect.fintype.html#4102da6205bd8605932488256a8bd517"><span class="id" title="notation">subset</span></a> <a class="idref" href="mathcomp.ssreflect.finset.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#f92718946b2f68c8f7100be4d6b45f82"><span class="id" title="notation">}</span></a>.<br/> - -<br/> -<span class="id" title="keyword">End</span> <a class="idref" href="mathcomp.ssreflect.finset.html#MaxSetMinSet"><span class="id" title="section">MaxSetMinSet</span></a>.<br/> - -<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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