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/csubt/getl.ma".
19 include "basic_1/pc3/left.ma".
22 \forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (t2: T).((pr2 c1
23 t1 t2) \to (\forall (c2: C).((csubt g c1 c2) \to (pr2 c2 t1 t2)))))))
25 \lambda (g: G).(\lambda (c1: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda
26 (H: (pr2 c1 t1 t2)).(let TMP_1 \def (\lambda (c: C).(\lambda (t: T).(\lambda
27 (t0: T).(\forall (c2: C).((csubt g c c2) \to (pr2 c2 t t0)))))) in (let TMP_2
28 \def (\lambda (c: C).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H0: (pr0 t3
29 t4)).(\lambda (c2: C).(\lambda (_: (csubt g c c2)).(pr2_free c2 t3 t4
30 H0))))))) in (let TMP_9 \def (\lambda (c: C).(\lambda (d: C).(\lambda (u:
31 T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr)
32 u))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H1: (pr0 t3 t4)).(\lambda
33 (t: T).(\lambda (H2: (subst0 i u t4 t)).(\lambda (c2: C).(\lambda (H3: (csubt
34 g c c2)).(let H4 \def (csubt_getl_abbr g c d u i H0 c2 H3) in (let TMP_3 \def
35 (\lambda (d2: C).(csubt g d d2)) in (let TMP_6 \def (\lambda (d2: C).(let
36 TMP_4 \def (Bind Abbr) in (let TMP_5 \def (CHead d2 TMP_4 u) in (getl i c2
37 TMP_5)))) in (let TMP_7 \def (pr2 c2 t3 t) in (let TMP_8 \def (\lambda (x:
38 C).(\lambda (_: (csubt g d x)).(\lambda (H6: (getl i c2 (CHead x (Bind Abbr)
39 u))).(pr2_delta c2 x u i H6 t3 t4 H1 t H2)))) in (ex2_ind C TMP_3 TMP_6 TMP_7
40 TMP_8 H4)))))))))))))))))) in (pr2_ind TMP_1 TMP_2 TMP_9 c1 t1 t2 H)))))))).
43 \forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (t2: T).((pc3 c1
44 t1 t2) \to (\forall (c2: C).((csubt g c1 c2) \to (pc3 c2 t1 t2)))))))
46 \lambda (g: G).(\lambda (c1: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda
47 (H: (pc3 c1 t1 t2)).(let TMP_1 \def (\lambda (t: T).(\lambda (t0: T).(\forall
48 (c2: C).((csubt g c1 c2) \to (pc3 c2 t t0))))) in (let TMP_2 \def (\lambda
49 (t: T).(\lambda (c2: C).(\lambda (_: (csubt g c1 c2)).(pc3_refl c2 t)))) in
50 (let TMP_6 \def (\lambda (t0: T).(\lambda (t3: T).(\lambda (H0: (pr2 c1 t0
51 t3)).(\lambda (t4: T).(\lambda (_: (pc3 c1 t3 t4)).(\lambda (H2: ((\forall
52 (c2: C).((csubt g c1 c2) \to (pc3 c2 t3 t4))))).(\lambda (c2: C).(\lambda
53 (H3: (csubt g c1 c2)).(let TMP_3 \def (csubt_pr2 g c1 t0 t3 H0 c2 H3) in (let
54 TMP_4 \def (pc3_pr2_r c2 t0 t3 TMP_3) in (let TMP_5 \def (H2 c2 H3) in (pc3_t
55 t3 c2 t0 TMP_4 t4 TMP_5)))))))))))) in (let TMP_10 \def (\lambda (t0:
56 T).(\lambda (t3: T).(\lambda (H0: (pr2 c1 t0 t3)).(\lambda (t4: T).(\lambda
57 (_: (pc3 c1 t0 t4)).(\lambda (H2: ((\forall (c2: C).((csubt g c1 c2) \to (pc3
58 c2 t0 t4))))).(\lambda (c2: C).(\lambda (H3: (csubt g c1 c2)).(let TMP_7 \def
59 (csubt_pr2 g c1 t0 t3 H0 c2 H3) in (let TMP_8 \def (pc3_pr2_x c2 t3 t0 TMP_7)
60 in (let TMP_9 \def (H2 c2 H3) in (pc3_t t0 c2 t3 TMP_8 t4 TMP_9))))))))))))
61 in (pc3_ind_left c1 TMP_1 TMP_2 TMP_6 TMP_10 t1 t2 H))))))))).