| 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. A \lor \not A.
+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
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).
+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.
+