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 *)
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15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1/csubv/defs.ma".
19 include "basic_1/C/fwd.ma".
21 include "basic_1/T/props.ma".
23 theorem csubv_bind_same:
24 \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (b: B).(\forall
25 (v1: T).(\forall (v2: T).(csubv (CHead c1 (Bind b) v1) (CHead c2 (Bind b)
28 \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubv c1 c2)).(\lambda (b:
29 B).(let TMP_5 \def (\lambda (b0: B).(\forall (v1: T).(\forall (v2: T).(let
30 TMP_1 \def (Bind b0) in (let TMP_2 \def (CHead c1 TMP_1 v1) in (let TMP_3
31 \def (Bind b0) in (let TMP_4 \def (CHead c2 TMP_3 v2) in (csubv TMP_2
32 TMP_4)))))))) in (let TMP_6 \def (\lambda (v1: T).(\lambda (v2:
33 T).(csubv_bind c1 c2 H Abbr not_abbr_void Abbr v1 v2))) in (let TMP_7 \def
34 (\lambda (v1: T).(\lambda (v2: T).(csubv_bind c1 c2 H Abst not_abst_void Abst
35 v1 v2))) in (let TMP_8 \def (\lambda (v1: T).(\lambda (v2: T).(csubv_void c1
36 c2 H v1 v2))) in (B_ind TMP_5 TMP_6 TMP_7 TMP_8 b)))))))).
39 \forall (c: C).(csubv c c)
41 \lambda (c: C).(let TMP_1 \def (\lambda (c0: C).(csubv c0 c0)) in (let TMP_2
42 \def (\lambda (n: nat).(csubv_sort n)) in (let TMP_8 \def (\lambda (c0:
43 C).(\lambda (H: (csubv c0 c0)).(\lambda (k: K).(let TMP_5 \def (\lambda (k0:
44 K).(\forall (t: T).(let TMP_3 \def (CHead c0 k0 t) in (let TMP_4 \def (CHead
45 c0 k0 t) in (csubv TMP_3 TMP_4))))) in (let TMP_6 \def (\lambda (b:
46 B).(\lambda (t: T).(csubv_bind_same c0 c0 H b t t))) in (let TMP_7 \def
47 (\lambda (f: F).(\lambda (t: T).(csubv_flat c0 c0 H f f t t))) in (K_ind
48 TMP_5 TMP_6 TMP_7 k))))))) in (C_ind TMP_1 TMP_2 TMP_8 c)))).