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 ≝
interpretation "multiple existental quantifier (6, 7)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_7 ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+(* multiple existental quantifier (6, 8) *)
+
+inductive ex6_8 (A0,A1,A2,A3,A4,A5,A6,A7:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A2→A3→A4→A5→A6→A7→Prop) : Prop ≝
+ | ex6_8_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7. P0 x0 x1 x2 x3 x4 x5 x6 x7 → P1 x0 x1 x2 x3 x4 x5 x6 x7 → P2 x0 x1 x2 x3 x4 x5 x6 x7 → P3 x0 x1 x2 x3 x4 x5 x6 x7 → P4 x0 x1 x2 x3 x4 x5 x6 x7 → P5 x0 x1 x2 x3 x4 x5 x6 x7 → ex6_8 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (6, 8)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_8 ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+
+(* multiple existental quantifier (6, 9) *)
+
+inductive ex6_9 (A0,A1,A2,A3,A4,A5,A6,A7,A8:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A2→A3→A4→A5→A6→A7→A8→Prop) : Prop ≝
+ | ex6_9_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 → ex6_9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (6, 9)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_9 ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+
+(* multiple existental quantifier (7, 3) *)
+
+inductive ex7_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→Prop) : Prop ≝
+ | ex7_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → P4 x0 x1 x2 → P5 x0 x1 x2 → P6 x0 x1 x2 → ex7_3 ? ? ? ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (7, 3)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_3 ? ? ? P0 P1 P2 P3 P4 P5 P6).
+
(* multiple existental quantifier (7, 4) *)
inductive ex7_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→A3→Prop) : Prop ≝
interpretation "multiple existental quantifier (7, 4)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_4 ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+(* multiple existental quantifier (7, 5) *)
+
+inductive ex7_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→A3→A4→Prop) : Prop ≝
+ | ex7_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 → P3 x0 x1 x2 x3 x4 → P4 x0 x1 x2 x3 x4 → P5 x0 x1 x2 x3 x4 → P6 x0 x1 x2 x3 x4 → ex7_5 ? ? ? ? ? ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (7, 5)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+
(* multiple existental quantifier (7, 7) *)
inductive ex7_7 (A0,A1,A2,A3,A4,A5,A6:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→A3→A4→A5→A6→Prop) : Prop ≝
interpretation "multiple existental quantifier (7, 7)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_7 ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
-(* multiple existental quantifier (8, 5) *)
+(* multiple existental quantifier (7, 9) *)
-inductive ex8_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7:A0→A1→A2→A3→A4→Prop) : Prop ≝
- | ex8_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 → P3 x0 x1 x2 x3 x4 → P4 x0 x1 x2 x3 x4 → P5 x0 x1 x2 x3 x4 → P6 x0 x1 x2 x3 x4 → P7 x0 x1 x2 x3 x4 → ex8_5 ? ? ? ? ? ? ? ? ? ? ? ? ?
+inductive ex7_9 (A0,A1,A2,A3,A4,A5,A6,A7,A8:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→A3→A4→A5→A6→A7→A8→Prop) : Prop ≝
+ | ex7_9_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P6 x0 x1 x2 x3 x4 x5 x6 x7 x8 → ex7_9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
.
-interpretation "multiple existental quantifier (8, 5)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
+interpretation "multiple existental quantifier (7, 9)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_9 ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+
+(* multiple existental quantifier (7, 10) *)
+
+inductive ex7_10 (A0,A1,A2,A3,A4,A5,A6,A7,A8,A9:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→A3→A4→A5→A6→A7→A8→A9→Prop) : Prop ≝
+ | ex7_10_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8,x9. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P6 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → ex7_10 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
+.
-(* multiple existental quantifier (9, 3) *)
+interpretation "multiple existental quantifier (7, 10)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_10 ? ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
-inductive ex9_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7,P8:A0→A1→A2→Prop) : Prop ≝
- | ex9_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → P4 x0 x1 x2 → P5 x0 x1 x2 → P6 x0 x1 x2 → P7 x0 x1 x2 → P8 x0 x1 x2 → ex9_3 ? ? ? ? ? ? ? ? ? ? ? ?
+(* multiple existental quantifier (8, 4) *)
+
+inductive ex8_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7:A0→A1→A2→A3→Prop) : Prop ≝
+ | ex8_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → P3 x0 x1 x2 x3 → P4 x0 x1 x2 x3 → P5 x0 x1 x2 x3 → P6 x0 x1 x2 x3 → P7 x0 x1 x2 x3 → ex8_4 ? ? ? ? ? ? ? ? ? ? ? ?
.
-interpretation "multiple existental quantifier (9, 3)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 P8 = (ex9_3 ? ? ? P0 P1 P2 P3 P4 P5 P6 P7 P8).
+interpretation "multiple existental quantifier (8, 4)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_4 ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
+
+(* multiple existental quantifier (8, 5) *)
+
+inductive ex8_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7:A0→A1→A2→A3→A4→Prop) : Prop ≝
+ | ex8_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 → P3 x0 x1 x2 x3 x4 → P4 x0 x1 x2 x3 x4 → P5 x0 x1 x2 x3 x4 → P6 x0 x1 x2 x3 x4 → P7 x0 x1 x2 x3 x4 → ex8_5 ? ? ? ? ? ? ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (8, 5)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
-(* multiple existental quantifier (10, 4) *)
+(* multiple existental quantifier (8, 10) *)
-inductive ex10_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7,P8,P9:A0→A1→A2→A3→Prop) : Prop ≝
- | ex10_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → P3 x0 x1 x2 x3 → P4 x0 x1 x2 x3 → P5 x0 x1 x2 x3 → P6 x0 x1 x2 x3 → P7 x0 x1 x2 x3 → P8 x0 x1 x2 x3 → P9 x0 x1 x2 x3 → ex10_4 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
+inductive ex8_10 (A0,A1,A2,A3,A4,A5,A6,A7,A8,A9:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7:A0→A1→A2→A3→A4→A5→A6→A7→A8→A9→Prop) : Prop ≝
+ | ex8_10_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8,x9. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P6 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P7 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → ex8_10 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
.
-interpretation "multiple existental quantifier (10, 4)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 P8 P9 = (ex10_4 ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7 P8 P9).
+interpretation "multiple existental quantifier (8, 10)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_10 ? ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
(* multiple disjunction connective (3) *)