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Diffstat (limited to 'theories7/Logic/Decidable.v')
| -rw-r--r-- | theories7/Logic/Decidable.v | 58 |
1 files changed, 0 insertions, 58 deletions
diff --git a/theories7/Logic/Decidable.v b/theories7/Logic/Decidable.v deleted file mode 100644 index 537b5e88..00000000 --- a/theories7/Logic/Decidable.v +++ /dev/null @@ -1,58 +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: Decidable.v,v 1.1.2.1 2004/07/16 19:31:29 herbelin Exp $ i*) - -(** Properties of decidable propositions *) - -Definition decidable := [P:Prop] P \/ ~P. - -Theorem dec_not_not : (P:Prop)(decidable P) -> (~P -> False) -> P. -Unfold decidable; Tauto. -Qed. - -Theorem dec_True: (decidable True). -Unfold decidable; Auto. -Qed. - -Theorem dec_False: (decidable False). -Unfold decidable not; Auto. -Qed. - -Theorem dec_or: (A,B:Prop)(decidable A) -> (decidable B) -> (decidable (A\/B)). -Unfold decidable; Tauto. -Qed. - -Theorem dec_and: (A,B:Prop)(decidable A) -> (decidable B) ->(decidable (A/\B)). -Unfold decidable; Tauto. -Qed. - -Theorem dec_not: (A:Prop)(decidable A) -> (decidable ~A). -Unfold decidable; Tauto. -Qed. - -Theorem dec_imp: (A,B:Prop)(decidable A) -> (decidable B) ->(decidable (A->B)). -Unfold decidable; Tauto. -Qed. - -Theorem not_not : (P:Prop)(decidable P) -> (~(~P)) -> P. -Unfold decidable; Tauto. Qed. - -Theorem not_or : (A,B:Prop) ~(A\/B) -> ~A /\ ~B. -Tauto. Qed. - -Theorem not_and : (A,B:Prop) (decidable A) -> ~(A/\B) -> ~A \/ ~B. -Unfold decidable; Tauto. Qed. - -Theorem not_imp : (A,B:Prop) (decidable A) -> ~(A -> B) -> A /\ ~B. -Unfold decidable;Tauto. -Qed. - -Theorem imp_simp : (A,B:Prop) (decidable A) -> (A -> B) -> ~A \/ B. -Unfold decidable; Tauto. -Qed. - |