(* This code is copyrighted by its authors; it is distributed under  *)
(* the terms of the LGPL license (see LICENSE and description files) *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************************)
(*                                                                          *)
(*                                                                          *)
(*                   Solange Coupet-Grimal & Line Jakubiec                  *)
(*                                                                          *)
(*                                                                          *)
(*              Laboratoire d'Informatique de Marseille                     *)
(*               CMI-Technopole de Chateau-Gombert                          *)
(*                   39, Rue F. Joliot Curie                                *)
(*                   13453 MARSEILLE Cedex 13                               *)
(*           e-mail:{Solange.Coupet,Line.Jakubiec}@lim.univ-mrs.fr          *)
(*                                                                          *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              May 30th 1996                               *)
(*                                                                          *)
(****************************************************************************)
(*                                Lib_Bool.v                                *)
(****************************************************************************)
Require Export Bool.
Require Export IfProp.
(*Require Export Orb.*)
Require Export Zerob.
simple induction b; auto with bool.
Qed.
Hint Resolve bool_dec.
(************************************************************************)
simple induction a; simple induction b; auto with bool.
Qed.
Hint Immediate orb_sym.
simple induction a; simple induction b; auto with bool.
Qed.
Hint Resolve orb_false.
intros; elim (orb_false a b); auto with bool.
Qed.
intros; elim (orb_false a b); auto with bool.
Qed.
simple induction b1; auto with bool.
Qed.
(************************************************************************)
simple induction a; simple induction b; auto with bool.
Qed.
Hint Immediate and_sym.
simple induction a; simple induction b; auto with bool.
Qed.
simple induction a; simple induction b; auto with bool.
Qed.
intros; elim (andb_true a b); auto with bool.
Qed.
intros; elim (andb_true a b); auto with bool.
Qed.
simple induction b; auto with bool.
elim and_sym; auto with bool.
Qed.
intros a b.
elim and_sym; intros H.
apply andb_negb_true_r with b; auto with bool.
Qed.
(************************************************************************)

Lemma no_true_false : forall b : bool, b = false -> b <> true.