(* -*- coding:utf-8 -*- *)
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(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
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(* Logic *)
Notation "∀  x .. y , P" := (forall x, .. (forall y, P) ..)
  (at level 200, x binder, y binder, right associativity) : type_scope.
Notation "∃  x .. y , P" := (exists x, .. (exists y, P) ..)
  (at level 200, x binder, y binder, 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 *)
Notation "'λ'  x .. y , t" := (fun x => .. (fun y => t) ..)
  (at level 200, x binder, y binder, right associativity).

(* Arithmetic *)
Notation "x ≤ y" := (le x y) (at level 70, no associativity).
Notation "x ≥ y" := (ge x y) (at level 70, no associativity).

(* test *)
(*
Check ∀ x z, True -> (∃ y v, x + v ≥ y + z) ∨ x ≤ 0.
*)

(* Integer Arithmetic *)
(* TODO: this should come after ZArith
Notation "x ≤ y" := (Zle x y) (at level 70, no associativity).
*)