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(* -*- coding:utf-8 -*- *)
(************************************************************************)
(* 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 *)
(************************************************************************)
(* Logic *)
Notation "∀ x , P" := (forall x , P)
(at level 200, x ident, right associativity) : type_scope.
Notation "∀ x y , P" := (forall x y , P)
(at level 200, x ident, y ident, right associativity) : type_scope.
Notation "∀ x y z , P" := (forall x y z , P)
(at level 200, x ident, y ident, z ident, right associativity) : type_scope.
Notation "∀ x y z u , P" := (forall x y z u , P)
(at level 200, x ident, y ident, z ident, u ident, right associativity)
: type_scope.
Notation "∀ x : t , P" := (forall x : t , P)
(at level 200, x ident, right associativity) : type_scope.
Notation "∀ x y : t , P" := (forall x y : t , P)
(at level 200, x ident, y ident, right associativity) : type_scope.
Notation "∀ x y z : t , P" := (forall x y z : t , P)
(at level 200, x ident, y ident, z ident, right associativity) : type_scope.
Notation "∀ x y z u : t , P" := (forall x y z u : t , P)
(at level 200, x ident, y ident, z ident, u ident, right associativity)
: type_scope.
Notation "∃ x , P" := (exists x , P)
(at level 200, x ident, right associativity) : type_scope.
Notation "∃ x : t , P" := (exists x : t, P)
(at level 200, x ident, right associativity) : type_scope.
Notation "x ∨ y" := (x \/ y) (at level 85, right associativity) : type_scope.
Notation "x ∧ y" := (x /\ y) (at level 80, right associativity) : type_scope.
Notation "x → y" := (x -> y) (at level 90, right associativity): type_scope.
Notation "x ↔ y" := (x <-> y) (at level 95, no associativity): type_scope.
Notation "¬ x" := (~x) (at level 75, right associativity) : type_scope.
Notation "x ≠ y" := (x <> y) (at level 70) : type_scope.
(* Abstraction *)
(* Not nice
Notation "'λ' x : T , y" := ([x:T] y) (at level 1, x,T,y at level 10).
Notation "'λ' x := T , y" := ([x:=T] y) (at level 1, x,T,y at level 10).
*)
(* Arithmetic *)
Notation "x ≤ y" := (le x y) (at level 70, no associativity).
Notation "x ≥ y" := (ge x y) (at level 70, no associativity).
(* test *)
(*
Goal ∀ x, True -> (∃ y , x ≥ y + 1) ∨ x ≤ 0.
*)
(* Integer Arithmetic *)
(* TODO: this should come after ZArith
Notation "x ≤ y" := (Zle x y) (at level 1, y at level 10).
*)
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