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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) : type_scope.
+Notation "∀ x y , P" := 
+  (forall x y , P) (at level 200, x ident, y ident) : type_scope.
+Notation "∀ x y z , P" := 
+  (forall x y z , P) (at level 200, x ident, y ident, z ident) : 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) : type_scope.
+Notation "∀ x : t , P" := 
+  (forall x : t , P) (at level 200, x ident) : type_scope.
+Notation "∀ x y : t , P" := 
+  (forall x y : t , P) (at level 200, x ident, y ident) : type_scope.
+Notation "∀ x y z : t , P" := 
+  (forall x y z : t , P) (at level 200, x ident, y ident, z ident) : 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) : type_scope.
+
+Notation "∃ x , P" := (exists x , P) (at level 200, x ident) : type_scope.
+Notation "∃ x : t , P" := (exists x : t, P) (at level 200, x ident) : 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.
+
+
+(* 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
+Notation "x ≤ y" := (Zle x y) (at level 1, y at level 10).
+*)