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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 *)
(************************************************************************)
(* $Id: Ring.v 5920 2004-07-16 20:01:26Z herbelin $ *)
Require Export Bool.
Require Export Ring_theory.
Require Export Quote.
Require Export Ring_normalize.
Require Export Ring_abstract.
(* 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 in |- *.
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 in |- *; tauto.
Defined.
Add Ring bool xorb andb true false (fun b:bool => b) eqb BoolTheory
[ true false ].
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