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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 *)
-(************************************************************************)
-
-(*i $Id: IfProp.v,v 1.1.2.1 2004/07/16 19:31:25 herbelin Exp $ i*)
-
-Require Bool.
-
-Inductive IfProp [A,B:Prop] : bool-> Prop
- := Iftrue : A -> (IfProp A B true)
- | Iffalse : B -> (IfProp A B false).
-
-Hints Resolve Iftrue Iffalse : bool v62.
-
-Lemma Iftrue_inv : (A,B:Prop)(b:bool) (IfProp A B b) -> b=true -> A.
-NewDestruct 1; Intros; Auto with bool.
-Case diff_true_false; Auto with bool.
-Qed.
-
-Lemma Iffalse_inv : (A,B:Prop)(b:bool) (IfProp A B b) -> b=false -> B.
-NewDestruct 1; Intros; Auto with bool.
-Case diff_true_false; Trivial with bool.
-Qed.
-
-Lemma IfProp_true : (A,B:Prop)(IfProp A B true) -> A.
-Intros.
-Inversion H.
-Assumption.
-Qed.
-
-Lemma IfProp_false : (A,B:Prop)(IfProp A B false) -> B.
-Intros.
-Inversion H.
-Assumption.
-Qed.
-
-Lemma IfProp_or : (A,B:Prop)(b:bool)(IfProp A B b) -> A\/B.
-NewDestruct 1; Auto with bool.
-Qed.
-
-Lemma IfProp_sum : (A,B:Prop)(b:bool)(IfProp A B b) -> {A}+{B}.
-NewDestruct b; Intro H.
-Left; Inversion H; Auto with bool.
-Right; Inversion H; Auto with bool.
-Qed.