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(************************************************************************)
(* 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 *)
(************************************************************************)
(*i $Id$ i*)
(** DisEquality is defined as the negation of equality *)
Require Params.
Require EqParams.
Require EqAxioms.
Definition neq : N -> N -> Prop := [x,y] ~(x=y).
Infix 6 "<>" neq V8only 70.
(* Proofs of axioms *)
Lemma eq_not_neq : (x,y:N)x=y->~(x<>y).
Unfold neq; Auto with num.
Qed.
Hints Immediate eq_not_neq : num.
Lemma neq_sym : (x,y:N)(x<>y)->(y<>x).
Unfold neq; Auto with num.
Qed.
Hints Resolve neq_sym : num.
Lemma neq_not_neq_trans : (x,y,z:N)(x<>y)->~(y<>z)->(x<>z).
Unfold neq; EAuto with num.
Qed.
Hints Resolve neq_not_neq_trans : num.
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