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affeldt-aist committed Jan 8, 2024
1 parent ed17518 commit 2f6c482
Showing 1 changed file with 21 additions and 21 deletions.
42 changes: 21 additions & 21 deletions classical/classical_sets.v
Original file line number Diff line number Diff line change
Expand Up @@ -33,29 +33,29 @@ From mathcomp Require Import mathcomp_extra boolp.
(* set (i.e., of type set rT) *)
(* - indexed sets are rather named F *)
(* *)
(* Sample notations: *)
(* Example of notations: *)
(* | Coq notations | | Meaning | *)
(* |-----------------------------:|---|:------------------------------------| *)
(* | set0 |==| $\emptyset$ | *)
(* | [set: A] |==| the full set of elements of type A | *)
(* | `` `\|` `` |==| $\cup$ | *)
(* | `` `&` `` |==| $\cap$ | *)
(* | `` `\` `` |==| set difference | *)
(* | `` ~` `` |==| set complement | *)
(* | `` `<=` `` |==| $\subseteq$ | *)
(* | `` f @` A `` |==| image by f of A | *)
(* | `` f @^-1` A `` |==| preimage by f of A | *)
(* | [set x] |==| the singleton set $\{x\}$ | *)
(* | [set~ x] |==| the complement of $\{x\}$ | *)
(* | [set E \| x in P] |==| the set of E with x ranging in P | *)
(* | range f |==| image by f of the full set | *)
(* | \big[setU/set0]_(i <- s \| P i) f i |==| finite union | *)
(* | \bigcup_(k in P) F k |==| countable union | *)
(* | \bigcap_(k in P) F k |==| countable intersection | *)
(* | trivIset D F |==| F is a sequence of pairwise disjoint | *)
(* | | | sets indexed over the domain D | *)
(* |-----------------------------:|---|:------------------------------------ *)
(* | set0 |==| $\emptyset$ *)
(* | [set: A] |==| the full set of elements of type A *)
(* | `` `\|` `` |==| $\cup$ *)
(* | `` `&` `` |==| $\cap$ *)
(* | `` `\` `` |==| set difference *)
(* | `` ~` `` |==| set complement *)
(* | `` `<=` `` |==| $\subseteq$ *)
(* | `` f @` A `` |==| image by f of A *)
(* | `` f @^-1` A `` |==| preimage by f of A *)
(* | [set x] |==| the singleton set $\{x\}$ *)
(* | [set~ x] |==| the complement of $\{x\}$ *)
(* | [set E \| x in P] |==| the set of E with x ranging in P *)
(* | range f |==| image by f of the full set *)
(* | \big[setU/set0]_(i <- s \| P i) f i |==| finite union *)
(* | \bigcup_(k in P) F k |==| countable union *)
(* | \bigcap_(k in P) F k |==| countable intersection *)
(* | trivIset D F |==| F is a sequence of pairwise disjoint *)
(* | | | sets indexed over the domain D *)
(* *)
(* Details: *)
(* Detailed documentation: *)
(* ## Sets *)
(* ``` *)
(* set T == type of sets on T *)
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