interpretation "multiple existental quantifier (3, 4)" 'Ex P0 P1 P2 = (ex3_4 ? ? ? ? P0 P1 P2).
+(* multiple existental quantifier (3, 5) *)
+
+inductive ex3_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2:A0→A1→A2→A3→A4→Prop) : Prop ≝
+ | ex3_5_intro: ∀x0,x1,x2,x3,x4. P0 x0 x1 x2 x3 x4 → P1 x0 x1 x2 x3 x4 → P2 x0 x1 x2 x3 x4 → ex3_5 ? ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (3, 5)" 'Ex P0 P1 P2 = (ex3_5 ? ? ? ? ? P0 P1 P2).
+
(* multiple existental quantifier (4, 1) *)
inductive ex4 (A0:Type[0]) (P0,P1,P2,P3:A0→Prop) : Prop ≝