interpretation "multiple existental quantifier (2, 2)" 'Ex P0 P1 = (ex2_2 ? ? P0 P1).
+(* multiple existental quantifier (2, 3) *)
+
+inductive ex2_3 (A0,A1,A2:Type[0]) (P0,P1:A0→A1→A2→Prop) : Prop ≝
+ | ex2_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → ex2_3 ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (2, 3)" 'Ex P0 P1 = (ex2_3 ? ? ? P0 P1).
+
(* multiple existental quantifier (3, 1) *)
inductive ex3_1 (A0:Type[0]) (P0,P1,P2:A0→Prop) : Prop ≝