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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1A/csubv/clear.ma".
19 include "basic_1A/csubv/drop.ma".
21 include "basic_1A/getl/fwd.ma".
23 lemma csubv_getl_conf:
24 \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (b1:
25 B).(\forall (d1: C).(\forall (v1: T).(\forall (i: nat).((getl i c1 (CHead d1
26 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_:
27 T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(getl
28 i c2 (CHead d2 (Bind b2) v2)))))))))))))
30 \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubv c1 c2)).(\lambda (b1:
31 B).(\lambda (d1: C).(\lambda (v1: T).(\lambda (i: nat).(\lambda (H0: (getl i
32 c1 (CHead d1 (Bind b1) v1))).(let H1 \def (getl_gen_all c1 (CHead d1 (Bind
33 b1) v1) i H0) in (ex2_ind C (\lambda (e: C).(drop i O c1 e)) (\lambda (e:
34 C).(clear e (CHead d1 (Bind b1) v1))) (ex2_3 B C T (\lambda (_: B).(\lambda
35 (d2: C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2:
36 C).(\lambda (v2: T).(getl i c2 (CHead d2 (Bind b2) v2)))))) (\lambda (x:
37 C).(\lambda (H2: (drop i O c1 x)).(\lambda (H3: (clear x (CHead d1 (Bind b1)
38 v1))).(let H_x \def (csubv_drop_conf c1 c2 H x i H2) in (let H4 \def H_x in
39 (ex2_ind C (\lambda (e2: C).(csubv x e2)) (\lambda (e2: C).(drop i O c2 e2))
40 (ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1
41 d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(getl i c2 (CHead
42 d2 (Bind b2) v2)))))) (\lambda (x0: C).(\lambda (H5: (csubv x x0)).(\lambda
43 (H6: (drop i O c2 x0)).(let H_x0 \def (csubv_clear_conf x x0 H5 b1 d1 v1 H3)
44 in (let H7 \def H_x0 in (ex2_3_ind B C T (\lambda (_: B).(\lambda (d2:
45 C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2:
46 C).(\lambda (v2: T).(clear x0 (CHead d2 (Bind b2) v2))))) (ex2_3 B C T
47 (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2)))) (\lambda
48 (b2: B).(\lambda (d2: C).(\lambda (v2: T).(getl i c2 (CHead d2 (Bind b2)
49 v2)))))) (\lambda (x1: B).(\lambda (x2: C).(\lambda (x3: T).(\lambda (H8:
50 (csubv d1 x2)).(\lambda (H9: (clear x0 (CHead x2 (Bind x1) x3))).(ex2_3_intro
51 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))))
52 (\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(getl i c2 (CHead d2 (Bind
53 b2) v2))))) x1 x2 x3 H8 (getl_intro i c2 (CHead x2 (Bind x1) x3) x0 H6
54 H9))))))) H7)))))) H4)))))) H1))))))))).
56 lemma csubv_getl_conf_void:
57 \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (d1:
58 C).(\forall (v1: T).(\forall (i: nat).((getl i c1 (CHead d1 (Bind Void) v1))
59 \to (ex2_2 C T (\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2:
60 C).(\lambda (v2: T).(getl i c2 (CHead d2 (Bind Void) v2)))))))))))
62 \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubv c1 c2)).(\lambda (d1:
63 C).(\lambda (v1: T).(\lambda (i: nat).(\lambda (H0: (getl i c1 (CHead d1
64 (Bind Void) v1))).(let H1 \def (getl_gen_all c1 (CHead d1 (Bind Void) v1) i
65 H0) in (ex2_ind C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: C).(clear e
66 (CHead d1 (Bind Void) v1))) (ex2_2 C T (\lambda (d2: C).(\lambda (_:
67 T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(getl i c2 (CHead d2
68 (Bind Void) v2))))) (\lambda (x: C).(\lambda (H2: (drop i O c1 x)).(\lambda
69 (H3: (clear x (CHead d1 (Bind Void) v1))).(let H_x \def (csubv_drop_conf c1
70 c2 H x i H2) in (let H4 \def H_x in (ex2_ind C (\lambda (e2: C).(csubv x e2))
71 (\lambda (e2: C).(drop i O c2 e2)) (ex2_2 C T (\lambda (d2: C).(\lambda (_:
72 T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(getl i c2 (CHead d2
73 (Bind Void) v2))))) (\lambda (x0: C).(\lambda (H5: (csubv x x0)).(\lambda
74 (H6: (drop i O c2 x0)).(let H_x0 \def (csubv_clear_conf_void x x0 H5 d1 v1
75 H3) in (let H7 \def H_x0 in (ex2_2_ind C T (\lambda (d2: C).(\lambda (_:
76 T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(clear x0 (CHead d2
77 (Bind Void) v2)))) (ex2_2 C T (\lambda (d2: C).(\lambda (_: T).(csubv d1
78 d2))) (\lambda (d2: C).(\lambda (v2: T).(getl i c2 (CHead d2 (Bind Void)
79 v2))))) (\lambda (x1: C).(\lambda (x2: T).(\lambda (H8: (csubv d1
80 x1)).(\lambda (H9: (clear x0 (CHead x1 (Bind Void) x2))).(ex2_2_intro C T
81 (\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda
82 (v2: T).(getl i c2 (CHead d2 (Bind Void) v2)))) x1 x2 H8 (getl_intro i c2
83 (CHead x1 (Bind Void) x2) x0 H6 H9)))))) H7)))))) H4)))))) H1)))))))).