diff options
Diffstat (limited to 'theories/Logic/Decidable.v')
| -rw-r--r-- | theories/Logic/Decidable.v | 26 |
1 files changed, 13 insertions, 13 deletions
diff --git a/theories/Logic/Decidable.v b/theories/Logic/Decidable.v index 00d63252..c6d32d9b 100644 --- a/theories/Logic/Decidable.v +++ b/theories/Logic/Decidable.v @@ -5,7 +5,7 @@ (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Decidable.v 11735 2009-01-02 17:22:31Z herbelin $ i*) +(*i $Id$ i*) (** Properties of decidable propositions *) @@ -13,7 +13,7 @@ Definition decidable (P:Prop) := P \/ ~ P. Theorem dec_not_not : forall P:Prop, decidable P -> (~ P -> False) -> P. Proof. -unfold decidable; tauto. +unfold decidable; tauto. Qed. Theorem dec_True : decidable True. @@ -29,27 +29,27 @@ Qed. Theorem dec_or : forall A B:Prop, decidable A -> decidable B -> decidable (A \/ B). Proof. -unfold decidable; tauto. +unfold decidable; tauto. Qed. Theorem dec_and : forall A B:Prop, decidable A -> decidable B -> decidable (A /\ B). Proof. -unfold decidable; tauto. +unfold decidable; tauto. Qed. Theorem dec_not : forall A:Prop, decidable A -> decidable (~ A). Proof. -unfold decidable; tauto. +unfold decidable; tauto. Qed. Theorem dec_imp : forall A B:Prop, decidable A -> decidable B -> decidable (A -> B). Proof. -unfold decidable; tauto. +unfold decidable; tauto. Qed. -Theorem dec_iff : +Theorem dec_iff : forall A B:Prop, decidable A -> decidable B -> decidable (A<->B). Proof. unfold decidable; tauto. @@ -67,7 +67,7 @@ Qed. Theorem not_and : forall A B:Prop, decidable A -> ~ (A /\ B) -> ~ A \/ ~ B. Proof. -unfold decidable; tauto. +unfold decidable; tauto. Qed. Theorem not_imp : forall A B:Prop, decidable A -> ~ (A -> B) -> A /\ ~ B. @@ -80,16 +80,16 @@ Proof. unfold decidable; tauto. Qed. -Theorem not_iff : - forall A B:Prop, decidable A -> decidable B -> +Theorem not_iff : + forall A B:Prop, decidable A -> decidable B -> ~ (A <-> B) -> (A /\ ~ B) \/ (~ A /\ B). Proof. unfold decidable; tauto. Qed. -(** Results formulated with iff, used in FSetDecide. - Negation are expanded since it is unclear whether setoid rewrite - will always perform conversion. *) +(** Results formulated with iff, used in FSetDecide. + Negation are expanded since it is unclear whether setoid rewrite + will always perform conversion. *) (** We begin with lemmas that, when read from left to right, can be understood as ways to eliminate uses of [not]. *) |