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 include "basic_1/getl/props.ma".
20 \forall (c: C).(\forall (i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda
21 (b: B).(\lambda (v: T).(getl i c (CHead e (Bind b) v)))))) (\forall (d:
22 C).((getl i c d) \to (\forall (P: Prop).P)))))
24 \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (i: nat).(or (ex_3 C B T
25 (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl i c0 (CHead e (Bind b)
26 v)))))) (\forall (d: C).((getl i c0 d) \to (\forall (P: Prop).P))))))
27 (\lambda (n: nat).(\lambda (i: nat).(or_intror (ex_3 C B T (\lambda (e:
28 C).(\lambda (b: B).(\lambda (v: T).(getl i (CSort n) (CHead e (Bind b)
29 v)))))) (\forall (d: C).((getl i (CSort n) d) \to (\forall (P: Prop).P)))
30 (\lambda (d: C).(\lambda (H: (getl i (CSort n) d)).(\lambda (P:
31 Prop).(getl_gen_sort n i d H P))))))) (\lambda (c0: C).(\lambda (H: ((\forall
32 (i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
33 T).(getl i c0 (CHead e (Bind b) v)))))) (\forall (d: C).((getl i c0 d) \to
34 (\forall (P: Prop).P))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (i:
35 nat).(nat_ind (\lambda (n: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b:
36 B).(\lambda (v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall
37 (d: C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))) (K_ind
38 (\lambda (k0: K).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
39 T).(getl O (CHead c0 k0 t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O
40 (CHead c0 k0 t) d) \to (\forall (P: Prop).P))))) (\lambda (b: B).(or_introl
41 (ex_3 C B T (\lambda (e: C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead
42 c0 (Bind b) t) (CHead e (Bind b0) v)))))) (\forall (d: C).((getl O (CHead c0
43 (Bind b) t) d) \to (\forall (P: Prop).P))) (ex_3_intro C B T (\lambda (e:
44 C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b) t) (CHead e
45 (Bind b0) v))))) c0 b t (getl_refl b c0 t)))) (\lambda (f: F).(let H_x \def
46 (H O) in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b:
47 B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v)))))) (\forall (d:
48 C).((getl O c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T (\lambda (e:
49 C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e
50 (Bind b) v)))))) (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to
51 (\forall (P: Prop).P)))) (\lambda (H1: (ex_3 C B T (\lambda (e: C).(\lambda
52 (b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v))))))).(ex_3_ind C B T
53 (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b)
54 v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl
55 O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O
56 (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P)))) (\lambda (x0:
57 C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl O c0 (CHead x0 (Bind
58 x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
59 T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d:
60 C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P))) (ex_3_intro
61 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat
62 f) t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_flat c0 (CHead x0 (Bind x1) x2)
63 O H2 f t))))))) H1)) (\lambda (H1: ((\forall (d: C).((getl O c0 d) \to
64 (\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e: C).(\lambda (b:
65 B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v))))))
66 (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P)))
67 (\lambda (d: C).(\lambda (H2: (getl O (CHead c0 (Flat f) t) d)).(\lambda (P:
68 Prop).(H1 d (getl_intro O c0 d c0 (drop_refl c0) (clear_gen_flat f c0 d t
69 (getl_gen_O (CHead c0 (Flat f) t) d H2))) P)))))) H0)))) k) (\lambda (n:
70 nat).(\lambda (_: (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda
71 (v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d:
72 C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))).(let H_x \def (H
73 (r k n)) in (let H1 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda
74 (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v)))))) (\forall
75 (d: C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T
76 (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t)
77 (CHead e (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to
78 (\forall (P: Prop).P)))) (\lambda (H2: (ex_3 C B T (\lambda (e: C).(\lambda
79 (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v))))))).(ex_3_ind
80 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead
81 e (Bind b) v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda
82 (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d:
83 C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P)))) (\lambda (x0:
84 C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H3: (getl (r k n) c0 (CHead x0
85 (Bind x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b:
86 B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v))))))
87 (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P)))
88 (ex_3_intro C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n)
89 (CHead c0 k t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_head k n c0 (CHead x0
90 (Bind x1) x2) H3 t))))))) H2)) (\lambda (H2: ((\forall (d: C).((getl (r k n)
91 c0 d) \to (\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e:
92 C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind
93 b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P:
94 Prop).P))) (\lambda (d: C).(\lambda (H3: (getl (S n) (CHead c0 k t)
95 d)).(\lambda (P: Prop).(H2 d (getl_gen_S k c0 d t n H3) P)))))) H1)))))