X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Flogic%2Fconnectives.ma;h=dacf542af2d7a6640f933d502b92cdd149ee6e24;hb=1e7db0c9a71cb3720d36ab090706a84e3f539fe0;hp=a5aab65f5d16fb77eda84a18be88e163802a86d2;hpb=9c8bb7e7c2548d2f37e5387cdce45df2b8fc9b43;p=helm.git diff --git a/helm/matita/library/logic/connectives.ma b/helm/matita/library/logic/connectives.ma index a5aab65f5..dacf542af 100644 --- a/helm/matita/library/logic/connectives.ma +++ b/helm/matita/library/logic/connectives.ma @@ -26,7 +26,12 @@ 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). +(*CSC: this alias should disappear. It is now required because the notation for Coq is pre-loaded *) +alias symbol "not" (instance 0) = "logical not". + +theorem absurd : \forall A,C:Prop. A \to \lnot A \to C. intros. elim (H1 H). qed. @@ -35,19 +40,29 @@ 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). +(*CSC: this alias should disappear. It is now required because the notation for Coq is pre-loaded *) +alias symbol "and" (instance 0) = "logical and". + +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). +(*CSC: this alias should disappear. It is now required because the notation for Coq is pre-loaded *) +alias symbol "or" (instance 0) = "logical or". -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.