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.
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 \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).
+
+notation < "hvbox(\exists ident i opt (: ty) break . p)"
+ right associative with precedence 20
+for @{ 'exists ${default
+ @{\lambda ${ident i} : $ty. $p)}
+ @{\lambda ${ident i} . $p}}}.
+
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.
+