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/csubc/drop.ma".
19 include "basic_1/csubc/clear.ma".
21 theorem csubc_getl_conf:
22 \forall (g: G).(\forall (c1: C).(\forall (e1: C).(\forall (i: nat).((getl i
23 c1 e1) \to (\forall (c2: C).((csubc g c1 c2) \to (ex2 C (\lambda (e2:
24 C).(getl i c2 e2)) (\lambda (e2: C).(csubc g e1 e2)))))))))
26 \lambda (g: G).(\lambda (c1: C).(\lambda (e1: C).(\lambda (i: nat).(\lambda
27 (H: (getl i c1 e1)).(\lambda (c2: C).(\lambda (H0: (csubc g c1 c2)).(let H1
28 \def (getl_gen_all c1 e1 i H) in (let TMP_1 \def (\lambda (e: C).(drop i O c1
29 e)) in (let TMP_2 \def (\lambda (e: C).(clear e e1)) in (let TMP_3 \def
30 (\lambda (e2: C).(getl i c2 e2)) in (let TMP_4 \def (\lambda (e2: C).(csubc g
31 e1 e2)) in (let TMP_5 \def (ex2 C TMP_3 TMP_4) in (let TMP_21 \def (\lambda
32 (x: C).(\lambda (H2: (drop i O c1 x)).(\lambda (H3: (clear x e1)).(let H_x
33 \def (csubc_drop_conf_O g c1 x i H2 c2 H0) in (let H4 \def H_x in (let TMP_6
34 \def (\lambda (e2: C).(drop i O c2 e2)) in (let TMP_7 \def (\lambda (e2:
35 C).(csubc g x e2)) in (let TMP_8 \def (\lambda (e2: C).(getl i c2 e2)) in
36 (let TMP_9 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_10 \def (ex2 C
37 TMP_8 TMP_9) in (let TMP_20 \def (\lambda (x0: C).(\lambda (H5: (drop i O c2
38 x0)).(\lambda (H6: (csubc g x x0)).(let H_x0 \def (csubc_clear_conf g x e1 H3
39 x0 H6) in (let H7 \def H_x0 in (let TMP_11 \def (\lambda (e2: C).(clear x0
40 e2)) in (let TMP_12 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_13
41 \def (\lambda (e2: C).(getl i c2 e2)) in (let TMP_14 \def (\lambda (e2:
42 C).(csubc g e1 e2)) in (let TMP_15 \def (ex2 C TMP_13 TMP_14) in (let TMP_19
43 \def (\lambda (x1: C).(\lambda (H8: (clear x0 x1)).(\lambda (H9: (csubc g e1
44 x1)).(let TMP_16 \def (\lambda (e2: C).(getl i c2 e2)) in (let TMP_17 \def
45 (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_18 \def (getl_intro i c2 x1 x0
46 H5 H8) in (ex_intro2 C TMP_16 TMP_17 x1 TMP_18 H9))))))) in (ex2_ind C TMP_11
47 TMP_12 TMP_15 TMP_19 H7)))))))))))) in (ex2_ind C TMP_6 TMP_7 TMP_10 TMP_20
48 H4)))))))))))) in (ex2_ind C TMP_1 TMP_2 TMP_5 TMP_21 H1)))))))))))))).