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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 *)
-(************************************************************************)
-
-(* Certification of Imperative Programs / Jean-Christophe Filliātre *)
-
-(* $Id: ProgBool.v 5920 2004-07-16 20:01:26Z herbelin $ *)
-
-Require Import ZArith.
-Require Export Bool_nat.
-Require Export Sumbool.
-
-Definition annot_bool :
- forall b:bool, {b' : bool | if b' then b = true else b = false}.
-Proof.
-intro b.
-exists b. case b; trivial.
-Qed.
-
-
-(* Logical connectives *)
-
-Definition spec_and (A B C D:Prop) (b:bool) := if b then A /\ C else B \/ D.
-
-Definition prog_bool_and :
- forall Q1 Q2:bool -> Prop,
- sig Q1 ->
- sig Q2 ->
- {b : bool | if b then Q1 true /\ Q2 true else Q1 false \/ Q2 false}.
-Proof.
-intros Q1 Q2 H1 H2.
-elim H1. intro b1. elim H2. intro b2.
-case b1; case b2; intros.
-exists true; auto.
-exists false; auto. exists false; auto. exists false; auto.
-Qed.
-
-Definition spec_or (A B C D:Prop) (b:bool) := if b then A \/ C else B /\ D.
-
-Definition prog_bool_or :
- forall Q1 Q2:bool -> Prop,
- sig Q1 ->
- sig Q2 ->
- {b : bool | if b then Q1 true \/ Q2 true else Q1 false /\ Q2 false}.
-Proof.
-intros Q1 Q2 H1 H2.
-elim H1. intro b1. elim H2. intro b2.
-case b1; case b2; intros.
-exists true; auto. exists true; auto. exists true; auto.
-exists false; auto.
-Qed.
-
-Definition spec_not (A B:Prop) (b:bool) := if b then B else A.
-
-Definition prog_bool_not :
- forall Q:bool -> Prop, sig Q -> {b : bool | if b then Q false else Q true}.
-Proof.
-intros Q H.
-elim H. intro b.
-case b; intro.
-exists false; auto. exists true; auto.
-Qed.