(* *********************************************************************)
(*                                                                     *)
(*              The Compcert verified compiler                         *)
(*                                                                     *)
(*          Jacques-Henri Jourdan, INRIA Paris-Rocquencourt            *)
(*                                                                     *)
(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the GNU General Public License as published by  *)
(*  the Free Software Foundation, either version 2 of the License, or  *)
(*  (at your option) any later version.  This file is also distributed *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
(*                                                                     *)
(* *********************************************************************)
Local Obligation Tactic := intros.
(** A comparable type is equiped with a [compare] function, that define an order relation. **)
Class Comparable (A:Type) := {
compare : A -> A -> comparison;
compare_antisym : forall x y, CompOpp (compare x y) = compare y x;
compare_trans :  forall x y z c,
(compare x y) = c -> (compare y z) = c -> (compare x z) = c
}.

Theorem compare_refl {A:Type} (C: Comparable A) :
forall x, compare x x = Eq.