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Library mathcomp.ssreflect.ssrnotations

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-(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.
- Distributed under the terms of CeCILL-B. *)
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Reserved notation for various arithmetic and algebraic operations: - e. [a1, ..., a_n] evaluation (e.g., polynomials). - e`i indexing (number list, integer pi-part). - x^-1 inverse (group, field). - x *+ n, x *- n integer multiplier (modules and rings). - x ^+ n, x ^- n integer exponent (groups and rings). - x *: A, A :* x external product (scaling/module product in rings, - left/right cosets in groups). - A :&: B intersection (of sets, groups, subspaces, ...). - A :|: B, a |: B union, union with a singleton (of sets). - A :\: B, A :\ b relative complement (of sets, subspaces, ...). - A, < [a]> generated group/subspace, generated cycle/line. - 'C[x], 'C_A[x] point centralisers (in groups and F-algebras). - 'C(A), 'C_B(A) centralisers (in groups and matrix and F_algebras). - 'Z(A) centers (in groups and matrix and F-algebras). - m %/ d, m %% d Euclidean division and remainder (nat, polynomials). - d %| m Euclidean divisibility (nat, polynomial). - m = n % [mod d] equality mod d (also defined for <>, ==, and !=). - e^`(n) nth formal derivative (groups, polynomials). - e^` simple formal derivative (polynomials only). - `|x| norm, absolute value, distance (rings, int, nat). - x <= y ?= iff C x is less than y, and equal iff C holds (nat, rings). - x <= y :> T, etc cast comparison (rings, all comparison operators). - [rec a1, ..., an] standard shorthand for hidden recursor (see prime.v). - The interpretation of these notations is not defined here, but the - declarations help maintain consistency across the library. -

- - Reserved notation for evaluation -

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-Reserved Notation "e .[ x ]"
-  (at level 2, left associativity, format "e .[ x ]").
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-Reserved Notation "e .[ x1 , x2 , .. , xn ]" (at level 2, left associativity,
-  format "e '[ ' .[ x1 , '/' x2 , '/' .. , '/' xn ] ']'").
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- Reserved notation for subscripting and superscripting -
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-Reserved Notation "s `_ i" (at level 3, i at level 2, left associativity,
-  format "s `_ i").
-Reserved Notation "x ^-1" (at level 3, left associativity, format "x ^-1").
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- Reserved notation for integer multipliers and exponents -
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-Reserved Notation "x *+ n" (at level 40, left associativity).
-Reserved Notation "x *- n" (at level 40, left associativity).
-Reserved Notation "x ^+ n" (at level 29, left associativity).
-Reserved Notation "x ^- n" (at level 29, left associativity).
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- Reserved notation for external multiplication. -
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-Reserved Notation "x *: A" (at level 40).
-Reserved Notation "A :* x" (at level 40).
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- Reserved notation for set-theretic operations. -
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-Reserved Notation "A :&: B" (at level 48, left associativity).
-Reserved Notation "A :|: B" (at level 52, left associativity).
-Reserved Notation "a |: A" (at level 52, left associativity).
-Reserved Notation "A :\: B" (at level 50, left associativity).
-Reserved Notation "A :\ b" (at level 50, left associativity).
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- Reserved notation for generated structures -
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-Reserved Notation "<< A >>" (at level 0, format "<< A >>").
-Reserved Notation "<[ a ] >" (at level 0, format "<[ a ] >").
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- Reserved notation for centralisers and centers. -
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-Reserved Notation "''C' [ x ]" (at level 8, format "''C' [ x ]").
-Reserved Notation "''C_' A [ x ]"
-  (at level 8, A at level 2, format "''C_' A [ x ]").
-Reserved Notation "''C' ( A )" (at level 8, format "''C' ( A )").
-Reserved Notation "''C_' B ( A )"
-  (at level 8, B at level 2, format "''C_' B ( A )").
-Reserved Notation "''Z' ( A )" (at level 8, format "''Z' ( A )").
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- Compatibility with group action centraliser notation. -
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-Reserved Notation "''C_' ( A ) [ x ]" (at level 8, only parsing).
-Reserved Notation "''C_' ( B ) ( A )" (at level 8, only parsing).
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- Reserved notation for Euclidean division and divisibility. -
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-Reserved Notation "m %/ d" (at level 40, no associativity).
-Reserved Notation "m %% d" (at level 40, no associativity).
-Reserved Notation "m %| d" (at level 70, no associativity).
-Reserved Notation "m = n %[mod d ]" (at level 70, n at next level,
-  format "'[hv ' m '/' = n '/' %[mod d ] ']'").
-Reserved Notation "m == n %[mod d ]" (at level 70, n at next level,
-  format "'[hv ' m '/' == n '/' %[mod d ] ']'").
-Reserved Notation "m <> n %[mod d ]" (at level 70, n at next level,
-  format "'[hv ' m '/' <> n '/' %[mod d ] ']'").
-Reserved Notation "m != n %[mod d ]" (at level 70, n at next level,
-  format "'[hv ' m '/' != n '/' %[mod d ] ']'").
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- Reserved notation for derivatives. -
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-Reserved Notation "a ^` " (at level 8, format "a ^` ").
-Reserved Notation "a ^` ( n )" (at level 8, format "a ^` ( n )").
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- Reserved notation for absolute value. -
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-Reserved Notation "`| x |" (at level 0, x at level 99, format "`| x |").
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- Reserved notation for conditional comparison -
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-Reserved Notation "x <= y ?= 'iff' c" (at level 70, y, c at next level,
-  format "x '[hv' <= y '/' ?= 'iff' c ']'").
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- Reserved notation for cast comparison. -
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-Reserved Notation "x <= y :> T" (at level 70, y at next level).
-Reserved Notation "x >= y :> T" (at level 70, y at next level, only parsing).
-Reserved Notation "x < y :> T" (at level 70, y at next level).
-Reserved Notation "x > y :> T" (at level 70, y at next level, only parsing).
-Reserved Notation "x <= y ?= 'iff' c :> T" (at level 70, y, c at next level,
-  format "x '[hv' <= y '/' ?= 'iff' c :> T ']'").
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