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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2003-11-29 17:28:49 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2003-11-29 17:28:49 +0000
commit9a6e3fe764dc2543dfa94de20fe5eec42d6be705 (patch)
tree77c0021911e3696a8c98e35a51840800db4be2a9 /theories/Logic/Decidable.v
parent9058fb97426307536f56c3e7447be2f70798e081 (diff)
Remplacement des fichiers .v ancienne syntaxe de theories, contrib et states par les fichiers nouvelle syntaxe
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5027 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/Decidable.v')
-rw-r--r--theories/Logic/Decidable.v54
1 files changed, 28 insertions, 26 deletions
diff --git a/theories/Logic/Decidable.v b/theories/Logic/Decidable.v
index 82464b3af..ebc21f755 100644
--- a/theories/Logic/Decidable.v
+++ b/theories/Logic/Decidable.v
@@ -9,50 +9,52 @@
(** Properties of decidable propositions *)
-Definition decidable := [P:Prop] P \/ ~P.
+Definition decidable (P:Prop) := P \/ ~ P.
-Theorem dec_not_not : (P:Prop)(decidable P) -> (~P -> False) -> P.
-Unfold decidable; Tauto.
+Theorem dec_not_not : forall P:Prop, decidable P -> (~ P -> False) -> P.
+unfold decidable in |- *; tauto.
Qed.
-Theorem dec_True: (decidable True).
-Unfold decidable; Auto.
+Theorem dec_True : decidable True.
+unfold decidable in |- *; auto.
Qed.
-Theorem dec_False: (decidable False).
-Unfold decidable not; Auto.
+Theorem dec_False : decidable False.
+unfold decidable, not in |- *; auto.
Qed.
-Theorem dec_or: (A,B:Prop)(decidable A) -> (decidable B) -> (decidable (A\/B)).
-Unfold decidable; Tauto.
+Theorem dec_or :
+ forall A B:Prop, decidable A -> decidable B -> decidable (A \/ B).
+unfold decidable in |- *; tauto.
Qed.
-Theorem dec_and: (A,B:Prop)(decidable A) -> (decidable B) ->(decidable (A/\B)).
-Unfold decidable; Tauto.
+Theorem dec_and :
+ forall A B:Prop, decidable A -> decidable B -> decidable (A /\ B).
+unfold decidable in |- *; tauto.
Qed.
-Theorem dec_not: (A:Prop)(decidable A) -> (decidable ~A).
-Unfold decidable; Tauto.
+Theorem dec_not : forall A:Prop, decidable A -> decidable (~ A).
+unfold decidable in |- *; tauto.
Qed.
-Theorem dec_imp: (A,B:Prop)(decidable A) -> (decidable B) ->(decidable (A->B)).
-Unfold decidable; Tauto.
+Theorem dec_imp :
+ forall A B:Prop, decidable A -> decidable B -> decidable (A -> B).
+unfold decidable in |- *; tauto.
Qed.
-Theorem not_not : (P:Prop)(decidable P) -> (~(~P)) -> P.
-Unfold decidable; Tauto. Qed.
+Theorem not_not : forall P:Prop, decidable P -> ~ ~ P -> P.
+unfold decidable in |- *; tauto. Qed.
-Theorem not_or : (A,B:Prop) ~(A\/B) -> ~A /\ ~B.
-Tauto. Qed.
+Theorem not_or : forall 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_and : forall A B:Prop, decidable A -> ~ (A /\ B) -> ~ A \/ ~ B.
+unfold decidable in |- *; tauto. Qed.
-Theorem not_imp : (A,B:Prop) (decidable A) -> ~(A -> B) -> A /\ ~B.
-Unfold decidable;Tauto.
+Theorem not_imp : forall A B:Prop, decidable A -> ~ (A -> B) -> A /\ ~ B.
+unfold decidable in |- *; tauto.
Qed.
-Theorem imp_simp : (A,B:Prop) (decidable A) -> (A -> B) -> ~A \/ B.
-Unfold decidable; Tauto.
+Theorem imp_simp : forall A B:Prop, decidable A -> (A -> B) -> ~ A \/ B.
+unfold decidable in |- *; tauto.
Qed.
-