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(* -*- coq-prog-args: ("-emacs-U") -*- *)
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* Custom notations and implicits for Coq prelude definitions.
*
* Author: Matthieu Sozeau
* Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
* 91405 Orsay, France *)
(** Notations for the unit type and value. *)
Notation " () " := Datatypes.unit : type_scope.
Notation " () " := tt.
(** Set maximally inserted implicit arguments for standard definitions. *)
Implicit Arguments eq [[A]].
Implicit Arguments Some [[A]].
Implicit Arguments None [[A]].
Implicit Arguments inl [[A] [B]].
Implicit Arguments inr [[A] [B]].
Implicit Arguments left [[A] [B]].
Implicit Arguments right [[A] [B]].
Require Import Coq.Lists.List.
Implicit Arguments nil [[A]].
Implicit Arguments cons [[A]].
(** Standard notations for lists. *)
Notation " [ ] " := nil : list_scope.
Notation " [ x ] " := (cons x nil) : list_scope.
Notation " [ x ; .. ; y ] " := (cons x .. (cons y nil) ..) : list_scope.
(** n-ary exists *)
Notation " 'exists' x y , p" := (ex (fun x => (ex (fun y => p))))
(at level 200, x ident, y ident, right associativity) : type_scope.
Notation " 'exists' x y z , p" := (ex (fun x => (ex (fun y => (ex (fun z => p))))))
(at level 200, x ident, y ident, z ident, right associativity) : type_scope.
Notation " 'exists' x y z w , p" := (ex (fun x => (ex (fun y => (ex (fun z => (ex (fun w => p))))))))
(at level 200, x ident, y ident, z ident, w ident, right associativity) : type_scope.
Tactic Notation "exist" constr(x) := exists x.
Tactic Notation "exist" constr(x) constr(y) := exists x ; exists y.
Tactic Notation "exist" constr(x) constr(y) constr(z) := exists x ; exists y ; exists z.
Tactic Notation "exist" constr(x) constr(y) constr(z) constr(w) := exists x ; exists y ; exists z ; exists w.
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