diff options
author | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-04-17 11:30:23 +0000 |
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committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-04-17 11:30:23 +0000 |
commit | cc1be0bf512b421336e81099aa6906ca47e4257a (patch) | |
tree | c25fa8ed965729d7a85efa3b3292fdf7f442963d /theories/Logic/Decidable.v | |
parent | ebf9aa9f97ef0d49ed1b799c9213f78efad4fec7 (diff) |
Uniformisation (Qed/Save et Implicits Arguments)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2650 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/Decidable.v')
-rw-r--r-- | theories/Logic/Decidable.v | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/Logic/Decidable.v b/theories/Logic/Decidable.v index 84649e7a8..82464b3af 100644 --- a/theories/Logic/Decidable.v +++ b/theories/Logic/Decidable.v @@ -13,46 +13,46 @@ Definition decidable := [P:Prop] P \/ ~P. Theorem dec_not_not : (P:Prop)(decidable P) -> (~P -> False) -> P. Unfold decidable; Tauto. -Save. +Qed. Theorem dec_True: (decidable True). Unfold decidable; Auto. -Save. +Qed. Theorem dec_False: (decidable False). Unfold decidable not; Auto. -Save. +Qed. Theorem dec_or: (A,B:Prop)(decidable A) -> (decidable B) -> (decidable (A\/B)). Unfold decidable; Tauto. -Save. +Qed. Theorem dec_and: (A,B:Prop)(decidable A) -> (decidable B) ->(decidable (A/\B)). Unfold decidable; Tauto. -Save. +Qed. Theorem dec_not: (A:Prop)(decidable A) -> (decidable ~A). Unfold decidable; Tauto. -Save. +Qed. Theorem dec_imp: (A,B:Prop)(decidable A) -> (decidable B) ->(decidable (A->B)). Unfold decidable; Tauto. -Save. +Qed. Theorem not_not : (P:Prop)(decidable P) -> (~(~P)) -> P. -Unfold decidable; Tauto. Save. +Unfold decidable; Tauto. Qed. Theorem not_or : (A,B:Prop) ~(A\/B) -> ~A /\ ~B. -Tauto. Save. +Tauto. Qed. Theorem not_and : (A,B:Prop) (decidable A) -> ~(A/\B) -> ~A \/ ~B. -Unfold decidable; Tauto. Save. +Unfold decidable; Tauto. Qed. Theorem not_imp : (A,B:Prop) (decidable A) -> ~(A -> B) -> A /\ ~B. Unfold decidable;Tauto. -Save. +Qed. Theorem imp_simp : (A,B:Prop) (decidable A) -> (A -> B) -> ~A \/ B. Unfold decidable; Tauto. -Save. +Qed. |