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Diffstat (limited to 'theories7/Bool/IfProp.v')
-rwxr-xr-x | theories7/Bool/IfProp.v | 49 |
1 files changed, 0 insertions, 49 deletions
diff --git a/theories7/Bool/IfProp.v b/theories7/Bool/IfProp.v deleted file mode 100755 index bcfa4be3..00000000 --- a/theories7/Bool/IfProp.v +++ /dev/null @@ -1,49 +0,0 @@ -(************************************************************************) -(* 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. |