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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was generated by xoa.native: do not edit *********************)
17 include "basics/pts.ma".
19 include "lambda/background/xoa_notation.ma".
21 (* multiple existental quantifier (1, 2) *)
23 inductive ex1_2 (A0,A1:Type[0]) (P0:A0→A1→Prop) : Prop ≝
24 | ex1_2_intro: ∀x0,x1. P0 x0 x1 → ex1_2 ? ? ?
27 interpretation "multiple existental quantifier (1, 2)" 'Ex P0 = (ex1_2 ? ? P0).
29 (* multiple existental quantifier (2, 2) *)
31 inductive ex2_2 (A0,A1:Type[0]) (P0,P1:A0→A1→Prop) : Prop ≝
32 | ex2_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → ex2_2 ? ? ? ?
35 interpretation "multiple existental quantifier (2, 2)" 'Ex P0 P1 = (ex2_2 ? ? P0 P1).
37 (* multiple existental quantifier (2, 3) *)
39 inductive ex2_3 (A0,A1,A2:Type[0]) (P0,P1:A0→A1→A2→Prop) : Prop ≝
40 | ex2_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → ex2_3 ? ? ? ? ?
43 interpretation "multiple existental quantifier (2, 3)" 'Ex P0 P1 = (ex2_3 ? ? ? P0 P1).
45 (* multiple existental quantifier (3, 1) *)
47 inductive ex3 (A0:Type[0]) (P0,P1,P2:A0→Prop) : Prop ≝
48 | ex3_intro: ∀x0. P0 x0 → P1 x0 → P2 x0 → ex3 ? ? ? ?
51 interpretation "multiple existental quantifier (3, 1)" 'Ex P0 P1 P2 = (ex3 ? P0 P1 P2).
53 (* multiple existental quantifier (3, 2) *)
55 inductive ex3_2 (A0,A1:Type[0]) (P0,P1,P2:A0→A1→Prop) : Prop ≝
56 | ex3_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → ex3_2 ? ? ? ? ?
59 interpretation "multiple existental quantifier (3, 2)" 'Ex P0 P1 P2 = (ex3_2 ? ? P0 P1 P2).
61 (* multiple existental quantifier (3, 3) *)
63 inductive ex3_3 (A0,A1,A2:Type[0]) (P0,P1,P2:A0→A1→A2→Prop) : Prop ≝
64 | ex3_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → ex3_3 ? ? ? ? ? ?
67 interpretation "multiple existental quantifier (3, 3)" 'Ex P0 P1 P2 = (ex3_3 ? ? ? P0 P1 P2).
69 (* multiple existental quantifier (3, 4) *)
71 inductive ex3_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2:A0→A1→A2→A3→Prop) : Prop ≝
72 | ex3_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → ex3_4 ? ? ? ? ? ? ?
75 interpretation "multiple existental quantifier (3, 4)" 'Ex P0 P1 P2 = (ex3_4 ? ? ? ? P0 P1 P2).
77 (* multiple existental quantifier (4, 1) *)
79 inductive ex4 (A0:Type[0]) (P0,P1,P2,P3:A0→Prop) : Prop ≝
80 | ex4_intro: ∀x0. P0 x0 → P1 x0 → P2 x0 → P3 x0 → ex4 ? ? ? ? ?
83 interpretation "multiple existental quantifier (4, 1)" 'Ex P0 P1 P2 P3 = (ex4 ? P0 P1 P2 P3).
85 (* multiple existental quantifier (4, 2) *)
87 inductive ex4_2 (A0,A1:Type[0]) (P0,P1,P2,P3:A0→A1→Prop) : Prop ≝
88 | ex4_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → P3 x0 x1 → ex4_2 ? ? ? ? ? ?
91 interpretation "multiple existental quantifier (4, 2)" 'Ex P0 P1 P2 P3 = (ex4_2 ? ? P0 P1 P2 P3).
93 (* multiple existental quantifier (4, 3) *)
95 inductive ex4_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3:A0→A1→A2→Prop) : Prop ≝
96 | ex4_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → ex4_3 ? ? ? ? ? ? ?
99 interpretation "multiple existental quantifier (4, 3)" 'Ex P0 P1 P2 P3 = (ex4_3 ? ? ? P0 P1 P2 P3).
101 (* multiple disjunction connective (3) *)
103 inductive or3 (P0,P1,P2:Prop) : Prop ≝
104 | or3_intro0: P0 → or3 ? ? ?
105 | or3_intro1: P1 → or3 ? ? ?
106 | or3_intro2: P2 → or3 ? ? ?
109 interpretation "multiple disjunction connective (3)" 'Or P0 P1 P2 = (or3 P0 P1 P2).