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/clear/props.ma".
21 include "Basic-1/flt/props.ma".
24 \forall (b: B).(\forall (c: C).(\forall (e: C).(\forall (u: T).(\forall (i:
25 nat).((getl i c (CHead e (Bind b) u)) \to (flt e u c (TLRef i)))))))
27 \lambda (b: B).(\lambda (c: C).(C_ind (\lambda (c0: C).(\forall (e:
28 C).(\forall (u: T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to
29 (flt e u c0 (TLRef i))))))) (\lambda (n: nat).(\lambda (e: C).(\lambda (u:
30 T).(\lambda (i: nat).(\lambda (H: (getl i (CSort n) (CHead e (Bind b)
31 u))).(getl_gen_sort n i (CHead e (Bind b) u) H (flt e u (CSort n) (TLRef
32 i)))))))) (\lambda (c0: C).(\lambda (H: ((\forall (e: C).(\forall (u:
33 T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to (flt e u c0 (TLRef
34 i)))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e: C).(\lambda (u:
35 T).(\lambda (i: nat).(nat_ind (\lambda (n: nat).((getl n (CHead c0 k t)
36 (CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef n)))) (\lambda (H0:
37 (getl O (CHead c0 k t) (CHead e (Bind b) u))).(K_ind (\lambda (k0: K).((clear
38 (CHead c0 k0 t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k0 t) (TLRef
39 O)))) (\lambda (b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e
40 (Bind b) u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 in C
41 return (\lambda (_: C).C) with [(CSort _) \Rightarrow e | (CHead c1 _ _)
42 \Rightarrow c1])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind
43 b0 c0 (CHead e (Bind b) u) t H1)) in ((let H3 \def (f_equal C B (\lambda (e0:
44 C).(match e0 in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b |
45 (CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with
46 [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e (Bind b) u)
47 (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in
48 ((let H4 \def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda
49 (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0]))
50 (CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e
51 (Bind b) u) t H1)) in (\lambda (H5: (eq B b b0)).(\lambda (H6: (eq C e
52 c0)).(eq_ind_r T t (\lambda (t0: T).(flt e t0 (CHead c0 (Bind b0) t) (TLRef
53 O))) (eq_ind_r C c0 (\lambda (c1: C).(flt c1 t (CHead c0 (Bind b0) t) (TLRef
54 O))) (eq_ind B b (\lambda (b1: B).(flt c0 t (CHead c0 (Bind b1) t) (TLRef
55 O))) (flt_arith0 (Bind b) c0 t O) b0 H5) e H6) u H4)))) H3)) H2)))) (\lambda
56 (f: F).(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e (Bind b)
57 u))).(flt_arith1 (Bind b) e c0 u (clear_cle c0 (CHead e (Bind b) u)
58 (clear_gen_flat f c0 (CHead e (Bind b) u) t H1)) (Flat f) t O))) k
59 (getl_gen_O (CHead c0 k t) (CHead e (Bind b) u) H0))) (\lambda (n:
60 nat).(\lambda (_: (((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (flt e u
61 (CHead c0 k t) (TLRef n))))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead
62 e (Bind b) u))).(let H_y \def (H e u (r k n) (getl_gen_S k c0 (CHead e (Bind
63 b) u) t n H1)) in (flt_arith2 e c0 u (r k n) H_y k t (S n)))))) i)))))))) c)).