X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flogic%2Fcoimplication.ma;h=a8fc4a232fbbcfc3eadca0a4476632f10bce23da;hb=7ce9eb0e973e414c988b416d118efe860516e275;hp=9edb4949c532c23ee43679ae11ad2ecac123d4bf;hpb=5e01cba364607e7937aec2e359c34f049bb0f108;p=helm.git diff --git a/helm/software/matita/library/logic/coimplication.ma b/helm/software/matita/library/logic/coimplication.ma index 9edb4949c..a8fc4a232 100644 --- a/helm/software/matita/library/logic/coimplication.ma +++ b/helm/software/matita/library/logic/coimplication.ma @@ -12,8 +12,6 @@ (* *) (**************************************************************************) -set "baseuri" "cic:/matita/logic/coimplication". - include "logic/connectives.ma". definition Iff : Prop \to Prop \to Prop \def @@ -31,17 +29,17 @@ notation < "hvbox(a break \leftrightarrow b)" for @{ 'iff $a $b }. theorem iff_intro: \forall A,B. (A \to B) \to (B \to A) \to (A \liff B). - unfold Iff. intros. split; intros; auto. + unfold Iff. intros. split; intros; autobatch. qed. theorem iff_refl: \forall A. A \liff A. - intros. apply iff_intro; intros; auto. + intros. apply iff_intro; intros; autobatch. qed. theorem iff_sym: \forall A,B. A \liff B \to B \liff A. - intros. decompose. apply iff_intro; intros; auto. + intros. elim H. apply iff_intro[assumption|assumption] qed. theorem iff_trans: \forall A,B,C. A \liff B \to B \liff C \to A \liff C. - intros. decompose. apply iff_intro; intros; auto. + intros. elim H. elim H1. apply iff_intro;intros;autobatch. qed.