Imported Upstream version 8.0pl1upstream/8.0pl1

1 files changed, 49 insertions, 0 deletions

diff --git a/theories7/Bool/IfProp.v b/theories7/Bool/IfProp.v
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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.