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).
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.
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.
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.