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/Level-1/LambdaDelta/getl/dec".
19 include "getl/props.ma".
22 \forall (c: C).(\forall (i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda
23 (b: B).(\lambda (v: T).(getl i c (CHead e (Bind b) v)))))) (\forall (d:
24 C).((getl i c d) \to (\forall (P: Prop).P)))))
26 \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (i: nat).(or (ex_3 C B T
27 (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl i c0 (CHead e (Bind b)
28 v)))))) (\forall (d: C).((getl i c0 d) \to (\forall (P: Prop).P))))))
29 (\lambda (n: nat).(\lambda (i: nat).(or_intror (ex_3 C B T (\lambda (e:
30 C).(\lambda (b: B).(\lambda (v: T).(getl i (CSort n) (CHead e (Bind b)
31 v)))))) (\forall (d: C).((getl i (CSort n) d) \to (\forall (P: Prop).P)))
32 (\lambda (d: C).(\lambda (H: (getl i (CSort n) d)).(\lambda (P:
33 Prop).(getl_gen_sort n i d H P))))))) (\lambda (c0: C).(\lambda (H: ((\forall
34 (i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
35 T).(getl i c0 (CHead e (Bind b) v)))))) (\forall (d: C).((getl i c0 d) \to
36 (\forall (P: Prop).P))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (i:
37 nat).(match i in nat return (\lambda (n: nat).(or (ex_3 C B T (\lambda (e:
38 C).(\lambda (b: B).(\lambda (v: T).(getl n (CHead c0 k t) (CHead e (Bind b)
39 v)))))) (\forall (d: C).((getl n (CHead c0 k t) d) \to (\forall (P:
40 Prop).P))))) with [O \Rightarrow (match k in K return (\lambda (k0: K).(or
41 (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0
42 k0 t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O (CHead c0 k0 t) d)
43 \to (\forall (P: Prop).P))))) with [(Bind b) \Rightarrow (or_introl (ex_3 C B
44 T (\lambda (e: C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b)
45 t) (CHead e (Bind b0) v)))))) (\forall (d: C).((getl O (CHead c0 (Bind b) t)
46 d) \to (\forall (P: Prop).P))) (ex_3_intro C B T (\lambda (e: C).(\lambda
47 (b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b) t) (CHead e (Bind b0)
48 v))))) c0 b t (getl_refl b c0 t))) | (Flat f) \Rightarrow (let H_x \def (H O)
49 in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b:
50 B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v)))))) (\forall (d:
51 C).((getl O c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T (\lambda (e:
52 C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e
53 (Bind b) v)))))) (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to
54 (\forall (P: Prop).P)))) (\lambda (H1: (ex_3 C B T (\lambda (e: C).(\lambda
55 (b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v))))))).(ex_3_ind C B T
56 (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b)
57 v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl
58 O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O
59 (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P)))) (\lambda (x0:
60 C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl O c0 (CHead x0 (Bind
61 x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
62 T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d:
63 C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P))) (ex_3_intro
64 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat
65 f) t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_flat c0 (CHead x0 (Bind x1) x2)
66 O H2 f t))))))) H1)) (\lambda (H1: ((\forall (d: C).((getl O c0 d) \to
67 (\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e: C).(\lambda (b:
68 B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v))))))
69 (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P)))
70 (\lambda (d: C).(\lambda (H2: (getl O (CHead c0 (Flat f) t) d)).(\lambda (P:
71 Prop).(H1 d (getl_intro O c0 d c0 (drop_refl c0) (clear_gen_flat f c0 d t
72 (getl_gen_O (CHead c0 (Flat f) t) d H2))) P)))))) H0)))]) | (S n) \Rightarrow
73 (let H_x \def (H (r k n)) in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda
74 (e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b)
75 v)))))) (\forall (d: C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))) (or
76 (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n)
77 (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead
78 c0 k t) d) \to (\forall (P: Prop).P)))) (\lambda (H1: (ex_3 C B T (\lambda
79 (e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b)
80 v))))))).(ex_3_ind C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
81 T).(getl (r k n) c0 (CHead e (Bind b) v))))) (or (ex_3 C B T (\lambda (e:
82 C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind
83 b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P:
84 Prop).P)))) (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2:
85 (getl (r k n) c0 (CHead x0 (Bind x1) x2))).(or_introl (ex_3 C B T (\lambda
86 (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e
87 (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall
88 (P: Prop).P))) (ex_3_intro C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
89 T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_head k
90 n c0 (CHead x0 (Bind x1) x2) H2 t))))))) H1)) (\lambda (H1: ((\forall (d:
91 C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))))).(or_intror (ex_3 C B T
92 (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t)
93 (CHead e (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to
94 (\forall (P: Prop).P))) (\lambda (d: C).(\lambda (H2: (getl (S n) (CHead c0 k
95 t) d)).(\lambda (P: Prop).(H1 d (getl_gen_S k c0 d t n H2) P))))))