(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
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Require Export Bool.
Require Export LegacyRing_theory.
Require Export Quote.
Require Export Ring_normalize.
Require Export Ring_abstract.
Declare ML Module "ring_plugin".

(* As an example, we provide an instantation for bool. *)
(* Other instatiations are given in ArithRing and ZArithRing in the
   same directory *)

Definition BoolTheory :
  Ring_Theory xorb andb true false (fun b:bool => b) eqb.
split; simpl.
destruct n; destruct m; reflexivity.
destruct n; destruct m; destruct p; reflexivity.
destruct n; destruct m; reflexivity.
destruct n; destruct m; destruct p; reflexivity.
destruct n; reflexivity.
destruct n; reflexivity.
destruct n; reflexivity.
destruct n; destruct m; destruct p; reflexivity.
destruct x; destruct y; reflexivity || simpl; tauto.
Defined.

Add Legacy Ring bool xorb andb true false (fun b:bool => b) eqb BoolTheory
 [ true false ].