-interpretation "constructive exists" 'exists \eta.x =
- (cic:/matita/dama/cprop_connectives/ex.ind#xpointer(1/1) _ x).
-
-interpretation "constructive exists (Type)" 'exists \eta.x =
- (cic:/matita/dama/cprop_connectives/exT.ind#xpointer(1/1) _ x).
+inductive exT23 (A:Type) (P:A→CProp) (Q:A→CProp) (R:A→A→CProp) : CProp ≝
+ ex_introT23: ∀w,p:A. P w → Q p → R w p → exT23 A P Q R.
+
+notation < "'fst' \nbsp x" non associative with precedence 50 for @{'pi1 $x}.
+notation < "'snd' \nbsp x" non associative with precedence 50 for @{'pi2 $x}.
+notation > "'fst' x" non associative with precedence 50 for @{'pi1 $x}.
+notation > "'snd' x" non associative with precedence 50 for @{'pi2 $x}.
+notation < "'fst' \nbsp x \nbsp y" non associative with precedence 50 for @{'pi12 $x $y}.
+notation < "'snd' \nbsp x \nbsp y" non associative with precedence 50 for @{'pi22 $x $y}.
+
+definition pi1exT ≝ λA,P.λx:exT A P.match x with [ex_introT x _ ⇒ x].
+
+interpretation "exT fst" 'pi1 x = (pi1exT _ _ x).
+interpretation "exT fst 2" 'pi12 x y = (pi1exT _ _ x y).
+
+definition pi1exT23 ≝
+ λA,P,Q,R.λx:exT23 A P Q R.match x with [ex_introT23 x _ _ _ _ ⇒ x].
+definition pi2exT23 ≝
+ λA,P,Q,R.λx:exT23 A P Q R.match x with [ex_introT23 _ x _ _ _ ⇒ x].
+
+interpretation "exT2 fst" 'pi1 x = (pi1exT23 _ _ _ _ x).
+interpretation "exT2 snd" 'pi2 x = (pi2exT23 _ _ _ _ x).
+interpretation "exT2 fst 2" 'pi12 x y = (pi1exT23 _ _ _ _ x y).
+interpretation "exT2 snd 2" 'pi22 x y = (pi2exT23 _ _ _ _ x y).