(*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).
-
+
+theorem Or_ind':
+ \forall A,B:Prop.
+ \forall P: A \lor B \to Prop.
+ (\forall p:A. P (or_introl ? ? p)) \to
+ (\forall q:B. P (or_intror ? ? q)) \to
+ \forall p:A \lor B. P p.
+ intros.
+ apply
+ (match p return \lambda p.P p with
+ [(or_introl p) \Rightarrow H p
+ |(or_intror q) \Rightarrow H1 q]).
+qed.
+
definition decidable : Prop \to Prop \def \lambda A:Prop. A \lor \lnot A.
inductive ex (A:Type) (P:A \to Prop) : Prop \def