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/ty3/arity.ma".
20 \forall (g: G).(\forall (c1: C).(\forall (c2: C).((csubt g c1 c2) \to (csuba
23 \lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubt g c1
24 c2)).(let TMP_1 \def (\lambda (c: C).(\lambda (c0: C).(csuba g c c0))) in
25 (let TMP_3 \def (\lambda (n: nat).(let TMP_2 \def (CSort n) in (csuba_refl g
26 TMP_2))) in (let TMP_4 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda (_:
27 (csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (k: K).(\lambda (u:
28 T).(csuba_head g c3 c4 H1 k u))))))) in (let TMP_5 \def (\lambda (c3:
29 C).(\lambda (c4: C).(\lambda (_: (csubt g c3 c4)).(\lambda (H1: (csuba g c3
30 c4)).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1:
31 T).(\lambda (u2: T).(csuba_void g c3 c4 H1 b H2 u1 u2))))))))) in (let TMP_16
32 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubt g c3 c4)).(\lambda
33 (H1: (csuba g c3 c4)).(\lambda (u: T).(\lambda (t: T).(\lambda (H2: (ty3 g c3
34 u t)).(\lambda (_: (ty3 g c4 u t)).(let H_x \def (ty3_arity g c3 u t H2) in
35 (let H4 \def H_x in (let TMP_6 \def (\lambda (a1: A).(arity g c3 u a1)) in
36 (let TMP_8 \def (\lambda (a1: A).(let TMP_7 \def (asucc g a1) in (arity g c3
37 t TMP_7))) in (let TMP_9 \def (Bind Abst) in (let TMP_10 \def (CHead c3 TMP_9
38 t) in (let TMP_11 \def (Bind Abbr) in (let TMP_12 \def (CHead c4 TMP_11 u) in
39 (let TMP_13 \def (csuba g TMP_10 TMP_12) in (let TMP_15 \def (\lambda (x:
40 A).(\lambda (H5: (arity g c3 u x)).(\lambda (H6: (arity g c3 t (asucc g
41 x))).(let TMP_14 \def (csuba_arity g c3 u x H5 c4 H1) in (csuba_abst g c3 c4
42 H1 t x H6 u TMP_14))))) in (ex2_ind A TMP_6 TMP_8 TMP_13 TMP_15
43 H4))))))))))))))))))) in (csubt_ind g TMP_1 TMP_3 TMP_4 TMP_5 TMP_16 c1 c2