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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-04-17 11:30:23 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-04-17 11:30:23 +0000
commitcc1be0bf512b421336e81099aa6906ca47e4257a (patch)
treec25fa8ed965729d7a85efa3b3292fdf7f442963d /theories/Logic/Decidable.v
parentebf9aa9f97ef0d49ed1b799c9213f78efad4fec7 (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.v24
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.