1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-1/types/defs".
19 include "preamble.ma".
21 inductive and3 (P0: Prop) (P1: Prop) (P2: Prop): Prop \def
22 | and3_intro: P0 \to (P1 \to (P2 \to (and3 P0 P1 P2))).
24 inductive or3 (P0: Prop) (P1: Prop) (P2: Prop): Prop \def
25 | or3_intro0: P0 \to (or3 P0 P1 P2)
26 | or3_intro1: P1 \to (or3 P0 P1 P2)
27 | or3_intro2: P2 \to (or3 P0 P1 P2).
29 inductive or4 (P0: Prop) (P1: Prop) (P2: Prop) (P3: Prop): Prop \def
30 | or4_intro0: P0 \to (or4 P0 P1 P2 P3)
31 | or4_intro1: P1 \to (or4 P0 P1 P2 P3)
32 | or4_intro2: P2 \to (or4 P0 P1 P2 P3)
33 | or4_intro3: P3 \to (or4 P0 P1 P2 P3).
35 inductive ex3 (A0: Set) (P0: A0 \to Prop) (P1: A0 \to Prop) (P2: A0 \to
37 | ex3_intro: \forall (x0: A0).((P0 x0) \to ((P1 x0) \to ((P2 x0) \to (ex3 A0
40 inductive ex4 (A0: Set) (P0: A0 \to Prop) (P1: A0 \to Prop) (P2: A0 \to Prop)
41 (P3: A0 \to Prop): Prop \def
42 | ex4_intro: \forall (x0: A0).((P0 x0) \to ((P1 x0) \to ((P2 x0) \to ((P3 x0)
43 \to (ex4 A0 P0 P1 P2 P3))))).
45 inductive ex_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)): Prop \def
46 | ex_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to (ex_2 A0 A1
49 inductive ex2_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)) (P1: A0 \to
50 (A1 \to Prop)): Prop \def
51 | ex2_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to ((P1 x0 x1)
52 \to (ex2_2 A0 A1 P0 P1)))).
54 inductive ex3_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)) (P1: A0 \to
55 (A1 \to Prop)) (P2: A0 \to (A1 \to Prop)): Prop \def
56 | ex3_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to ((P1 x0 x1)
57 \to ((P2 x0 x1) \to (ex3_2 A0 A1 P0 P1 P2))))).
59 inductive ex4_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)) (P1: A0 \to
60 (A1 \to Prop)) (P2: A0 \to (A1 \to Prop)) (P3: A0 \to (A1 \to Prop)): Prop
62 | ex4_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to ((P1 x0 x1)
63 \to ((P2 x0 x1) \to ((P3 x0 x1) \to (ex4_2 A0 A1 P0 P1 P2 P3)))))).
65 inductive ex_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to
67 | ex_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0 x1
68 x2) \to (ex_3 A0 A1 A2 P0)))).
70 inductive ex2_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to
71 Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))): Prop \def
72 | ex2_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0
73 x1 x2) \to ((P1 x0 x1 x2) \to (ex2_3 A0 A1 A2 P0 P1))))).
75 inductive ex3_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to
76 Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 \to
78 | ex3_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0
79 x1 x2) \to ((P1 x0 x1 x2) \to ((P2 x0 x1 x2) \to (ex3_3 A0 A1 A2 P0 P1
82 inductive ex4_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to
83 Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 \to
84 Prop))) (P3: A0 \to (A1 \to (A2 \to Prop))): Prop \def
85 | ex4_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0
86 x1 x2) \to ((P1 x0 x1 x2) \to ((P2 x0 x1 x2) \to ((P3 x0 x1 x2) \to (ex4_3 A0
87 A1 A2 P0 P1 P2 P3))))))).
89 inductive ex3_4 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (P0: A0 \to (A1 \to
90 (A2 \to (A3 \to Prop)))) (P1: A0 \to (A1 \to (A2 \to (A3 \to Prop)))) (P2: A0
91 \to (A1 \to (A2 \to (A3 \to Prop)))): Prop \def
92 | ex3_4_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall
93 (x3: A3).((P0 x0 x1 x2 x3) \to ((P1 x0 x1 x2 x3) \to ((P2 x0 x1 x2 x3) \to
94 (ex3_4 A0 A1 A2 A3 P0 P1 P2))))))).
96 inductive ex4_4 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (P0: A0 \to (A1 \to
97 (A2 \to (A3 \to Prop)))) (P1: A0 \to (A1 \to (A2 \to (A3 \to Prop)))) (P2: A0
98 \to (A1 \to (A2 \to (A3 \to Prop)))) (P3: A0 \to (A1 \to (A2 \to (A3 \to
100 | ex4_4_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall
101 (x3: A3).((P0 x0 x1 x2 x3) \to ((P1 x0 x1 x2 x3) \to ((P2 x0 x1 x2 x3) \to
102 ((P3 x0 x1 x2 x3) \to (ex4_4 A0 A1 A2 A3 P0 P1 P2 P3)))))))).
104 inductive ex4_5 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (P0: A0 \to
105 (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to
106 (A4 \to Prop))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P3:
107 A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))): Prop \def
108 | ex4_5_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall
109 (x3: A3).(\forall (x4: A4).((P0 x0 x1 x2 x3 x4) \to ((P1 x0 x1 x2 x3 x4) \to
110 ((P2 x0 x1 x2 x3 x4) \to ((P3 x0 x1 x2 x3 x4) \to (ex4_5 A0 A1 A2 A3 A4 P0 P1
113 inductive ex5_5 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (P0: A0 \to
114 (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to
115 (A4 \to Prop))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P3:
116 A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P4: A0 \to (A1 \to (A2 \to
117 (A3 \to (A4 \to Prop))))): Prop \def
118 | ex5_5_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall
119 (x3: A3).(\forall (x4: A4).((P0 x0 x1 x2 x3 x4) \to ((P1 x0 x1 x2 x3 x4) \to
120 ((P2 x0 x1 x2 x3 x4) \to ((P3 x0 x1 x2 x3 x4) \to ((P4 x0 x1 x2 x3 x4) \to
121 (ex5_5 A0 A1 A2 A3 A4 P0 P1 P2 P3 P4)))))))))).
123 inductive ex6_6 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (A5: Set)
124 (P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to Prop)))))) (P1: A0 \to
125 (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to Prop)))))) (P2: A0 \to (A1 \to (A2
126 \to (A3 \to (A4 \to (A5 \to Prop)))))) (P3: A0 \to (A1 \to (A2 \to (A3 \to
127 (A4 \to (A5 \to Prop)))))) (P4: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5
128 \to Prop)))))) (P5: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to
129 Prop)))))): Prop \def
130 | ex6_6_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall
131 (x3: A3).(\forall (x4: A4).(\forall (x5: A5).((P0 x0 x1 x2 x3 x4 x5) \to ((P1
132 x0 x1 x2 x3 x4 x5) \to ((P2 x0 x1 x2 x3 x4 x5) \to ((P3 x0 x1 x2 x3 x4 x5)
133 \to ((P4 x0 x1 x2 x3 x4 x5) \to ((P5 x0 x1 x2 x3 x4 x5) \to (ex6_6 A0 A1 A2
134 A3 A4 A5 P0 P1 P2 P3 P4 P5)))))))))))).
136 inductive ex6_7 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (A5: Set)
137 (A6: Set) (P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to
138 Prop))))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to
139 Prop))))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to
140 Prop))))))) (P3: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to
141 Prop))))))) (P4: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to
142 Prop))))))) (P5: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to
143 Prop))))))): Prop \def
144 | ex6_7_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall
145 (x3: A3).(\forall (x4: A4).(\forall (x5: A5).(\forall (x6: A6).((P0 x0 x1 x2
146 x3 x4 x5 x6) \to ((P1 x0 x1 x2 x3 x4 x5 x6) \to ((P2 x0 x1 x2 x3 x4 x5 x6)
147 \to ((P3 x0 x1 x2 x3 x4 x5 x6) \to ((P4 x0 x1 x2 x3 x4 x5 x6) \to ((P5 x0 x1
148 x2 x3 x4 x5 x6) \to (ex6_7 A0 A1 A2 A3 A4 A5 A6 P0 P1 P2 P3 P4