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/fwd.ma".
19 include "Basic-1/drop/props.ma".
21 include "Basic-1/clear/props.ma".
24 \forall (b: B).(\forall (c: C).(\forall (u: T).(getl O (CHead c (Bind b) u)
25 (CHead c (Bind b) u))))
27 \lambda (b: B).(\lambda (c: C).(\lambda (u: T).(getl_intro O (CHead c (Bind
28 b) u) (CHead c (Bind b) u) (CHead c (Bind b) u) (drop_refl (CHead c (Bind b)
29 u)) (clear_bind b c u)))).
35 \forall (k: K).(\forall (h: nat).(\forall (c: C).(\forall (e: C).((getl (r k
36 h) c e) \to (\forall (u: T).(getl (S h) (CHead c k u) e))))))
38 \lambda (k: K).(\lambda (h: nat).(\lambda (c: C).(\lambda (e: C).(\lambda
39 (H: (getl (r k h) c e)).(\lambda (u: T).(let H0 \def (getl_gen_all c e (r k
40 h) H) in (ex2_ind C (\lambda (e0: C).(drop (r k h) O c e0)) (\lambda (e0:
41 C).(clear e0 e)) (getl (S h) (CHead c k u) e) (\lambda (x: C).(\lambda (H1:
42 (drop (r k h) O c x)).(\lambda (H2: (clear x e)).(getl_intro (S h) (CHead c k
43 u) e x (drop_drop k h c x H1 u) H2)))) H0))))))).
49 \forall (c: C).(\forall (e: C).(\forall (h: nat).((getl h c e) \to (\forall
50 (f: F).(\forall (u: T).(getl h (CHead c (Flat f) u) e))))))
52 \lambda (c: C).(\lambda (e: C).(\lambda (h: nat).(\lambda (H: (getl h c
53 e)).(\lambda (f: F).(\lambda (u: T).(let H0 \def (getl_gen_all c e h H) in
54 (ex2_ind C (\lambda (e0: C).(drop h O c e0)) (\lambda (e0: C).(clear e0 e))
55 (getl h (CHead c (Flat f) u) e) (\lambda (x: C).(\lambda (H1: (drop h O c
56 x)).(\lambda (H2: (clear x e)).(nat_ind (\lambda (n: nat).((drop n O c x) \to
57 (getl n (CHead c (Flat f) u) e))) (\lambda (H3: (drop O O c x)).(let H4 \def
58 (eq_ind_r C x (\lambda (c0: C).(clear c0 e)) H2 c (drop_gen_refl c x H3)) in
59 (getl_intro O (CHead c (Flat f) u) e (CHead c (Flat f) u) (drop_refl (CHead c
60 (Flat f) u)) (clear_flat c e H4 f u)))) (\lambda (h0: nat).(\lambda (_:
61 (((drop h0 O c x) \to (getl h0 (CHead c (Flat f) u) e)))).(\lambda (H3: (drop
62 (S h0) O c x)).(getl_intro (S h0) (CHead c (Flat f) u) e x (drop_drop (Flat
63 f) h0 c x H3 u) H2)))) h H1)))) H0))))))).
69 \forall (b: B).(\forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i:
70 nat).((getl i c (CHead d (Bind b) u)) \to (\forall (k: K).(\forall (v:
71 T).(getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)))))))))
73 \lambda (b: B).(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
74 nat).(\lambda (H: (getl i c (CHead d (Bind b) u))).(\lambda (k: K).(\lambda
75 (v: T).(let H0 \def (getl_gen_all c (CHead d (Bind b) u) i H) in (ex2_ind C
76 (\lambda (e: C).(drop i O c e)) (\lambda (e: C).(clear e (CHead d (Bind b)
77 u))) (getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)) (\lambda (x:
78 C).(\lambda (H1: (drop i O c x)).(\lambda (H2: (clear x (CHead d (Bind b)
79 u))).(getl_intro i (CTail k v c) (CHead (CTail k v d) (Bind b) u) (CTail k v
80 x) (drop_ctail c x O i H1 k v) (clear_ctail b x d u H2 k v))))) H0))))))))).
86 \forall (c: C).(\forall (x1: C).(\forall (h: nat).((getl h c x1) \to
87 (\forall (x2: C).((getl h c x2) \to (eq C x1 x2))))))
89 \lambda (c: C).(\lambda (x1: C).(\lambda (h: nat).(\lambda (H: (getl h c
90 x1)).(\lambda (x2: C).(\lambda (H0: (getl h c x2)).(let H1 \def (getl_gen_all
91 c x2 h H0) in (ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e:
92 C).(clear e x2)) (eq C x1 x2) (\lambda (x: C).(\lambda (H2: (drop h O c
93 x)).(\lambda (H3: (clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in
94 (ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: C).(clear e x1)) (eq
95 C x1 x2) (\lambda (x0: C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear
96 x0 x1)).(let H7 \def (eq_ind C x (\lambda (c0: C).(drop h O c c0)) H2 x0
97 (drop_mono c x O h H2 x0 H5)) in (let H8 \def (eq_ind_r C x0 (\lambda (c0:
98 C).(drop h O c c0)) H7 x (drop_mono c x O h H2 x0 H5)) in (let H9 \def
99 (eq_ind_r C x0 (\lambda (c0: C).(clear c0 x1)) H6 x (drop_mono c x O h H2 x0
100 H5)) in (clear_mono x x1 H9 x2 H3))))))) H4))))) H1))))))).