X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Flogic%2Fconnectives.ma;h=6437bd132c6749b8ea44c58d6486e9f3d310cee0;hb=2ecd65dbcc1388bb2dfe6425e6ef1b2e3f45c4ac;hp=835bb68734c397f2ae6bdbc1e6ef5ed0a1b22e18;hpb=244d65f63ca6a736b871f9f91328fe8c5524ff05;p=helm.git diff --git a/helm/matita/library/logic/connectives.ma b/helm/matita/library/logic/connectives.ma index 835bb6873..6437bd132 100644 --- a/helm/matita/library/logic/connectives.ma +++ b/helm/matita/library/logic/connectives.ma @@ -12,45 +12,57 @@ (* *) (**************************************************************************) -set "baseuri" "cic:/matita/connectives/". +set "baseuri" "cic:/matita/logic/connectives/". inductive True: Prop \def I : True. -default "true" cic:/matita/logic/True.ind. +default "true" cic:/matita/logic/connectives/True.ind. inductive False: Prop \def . -default "false" cic:/matita/logic/False.ind. +default "false" cic:/matita/logic/connectives/False.ind. definition Not: Prop \to Prop \def \lambda A. (A \to False). -theorem absurd : \forall A,C:Prop. A \to Not A \to C. +(*CSC: the URI must disappear: there is a bug now *) +interpretation "logical not" 'not x = (cic:/matita/logic/connectives/Not.con x). + +theorem absurd : \forall A,C:Prop. A \to \lnot A \to C. intros. elim (H1 H). qed. -default "absurd" cic:/matita/logic/absurd.ind. +default "absurd" cic:/matita/logic/connectives/absurd.con. inductive And (A,B:Prop) : Prop \def conj : A \to B \to (And A B). -theorem proj1: \forall A,B:Prop. (And A B) \to A. +(*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). + +theorem proj1: \forall A,B:Prop. A \land B \to A. intros. elim H. assumption. qed. -theorem proj2: \forall A,B:Prop. (And A B) \to B. +theorem proj2: \forall A,B:Prop. A \land B \to B. intros. elim H. assumption. qed. 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). -definition decidable : Prop \to Prop \def \lambda A:Prop. Or A (Not A). +definition decidable : Prop \to Prop \def \lambda A:Prop. A \lor \not 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 x y = (cic:/matita/logic/connectives/ex.ind#xpointer(1/1) x y). + 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.