(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Require Export Ring_theory.
Require Export Ring_base.
Require Export InitialRing.
Require Export Ring_tac.
split; simpl.
destruct x; reflexivity.
destruct x; destruct y; reflexivity.
destruct x; destruct y; destruct z; reflexivity.
reflexivity.
destruct x; destruct y; reflexivity.
destruct x; destruct y; reflexivity.
destruct x; destruct y; destruct z; reflexivity.
reflexivity.
destruct x; reflexivity.
Qed.
Definition bool_eq (b1 b2:bool) :=
if b1 then b2 else negb b2.

Lemma bool_eq_ok : forall b1 b2, bool_eq b1 b2 = true -> b1 = b2.