X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flogic%2Fconnectives.ma;h=76d0323166ad947578481e7c06bb4d8d8b3cc41a;hb=e880d6eab5e1700f4a625ddcd7d0fa8f0cce2dcc;hp=5afc3e5dc29d7db0f45e812d244f6cd72e4ff7f6;hpb=c48de1fba2742df0d3ab42d69e758ae2859316d0;p=helm.git diff --git a/helm/software/matita/library/logic/connectives.ma b/helm/software/matita/library/logic/connectives.ma index 5afc3e5dc..76d032316 100644 --- a/helm/software/matita/library/logic/connectives.ma +++ b/helm/software/matita/library/logic/connectives.ma @@ -12,8 +12,6 @@ (* *) (**************************************************************************) -set "baseuri" "cic:/matita/logic/connectives/". - inductive True: Prop \def I : True. @@ -26,8 +24,7 @@ default "false" cic:/matita/logic/connectives/False.ind. definition Not: Prop \to Prop \def \lambda A. (A \to False). -(*CSC: the URI must disappear: there is a bug now *) -interpretation "logical not" 'not x = (cic:/matita/logic/connectives/Not.con x). +interpretation "logical not" 'not x = (Not x). theorem absurd : \forall A,C:Prop. A \to \lnot A \to C. intros. elim (H1 H). @@ -35,11 +32,16 @@ qed. default "absurd" cic:/matita/logic/connectives/absurd.con. +theorem not_to_not : \forall A,B:Prop. (A → B) \to ¬B →¬A. +intros.unfold.intro.apply H1.apply (H H2). +qed. + +default "absurd" cic:/matita/logic/connectives/absurd.con. + inductive And (A,B:Prop) : Prop \def conj : A \to B \to (And A B). -(*CSC: the URI must disappear: there is a bug now *) -interpretation "logical and" 'and x y = (cic:/matita/logic/connectives/And.ind#xpointer(1/1) x y). +interpretation "logical and" 'and x y = (And x y). theorem proj1: \forall A,B:Prop. A \land B \to A. intros. elim H. assumption. @@ -53,9 +55,7 @@ inductive Or (A,B:Prop) : Prop \def or_introl : A \to (Or A B) | or_intror : B \to (Or A B). -(*CSC: the URI must disappear: there is a bug now *) -interpretation "logical or" 'or x y = - (cic:/matita/logic/connectives/Or.ind#xpointer(1/1) x y). +interpretation "logical or" 'or x y = (Or x y). theorem Or_ind': \forall A,B:Prop. @@ -75,12 +75,10 @@ definition decidable : Prop \to Prop \def \lambda A:Prop. A \lor \lnot A. inductive ex (A:Type) (P:A \to Prop) : Prop \def ex_intro: \forall x:A. P x \to ex A P. -(*CSC: the URI must disappear: there is a bug now *) -interpretation "exists" 'exists \eta.x = - (cic:/matita/logic/connectives/ex.ind#xpointer(1/1) _ x). +interpretation "exists" 'exists x = (ex ? x). inductive ex2 (A:Type) (P,Q:A \to Prop) : Prop \def ex_intro2: \forall x:A. P x \to Q x \to ex2 A P Q. definition iff := - \lambda A,B. (A -> B) \land (B -> A). \ No newline at end of file + \lambda A,B. (A -> B) \land (B -> A).