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_1A/tlist/defs.ma".
20 \forall (k: K).(\forall (v: T).(\forall (t: T).(\forall (vs: TList).(eq T
21 (THeads k (TApp vs v) t) (THeads k vs (THead k v t))))))
23 \lambda (k: K).(\lambda (v: T).(\lambda (t: T).(\lambda (vs:
24 TList).(TList_ind (\lambda (t0: TList).(eq T (THeads k (TApp t0 v) t) (THeads
25 k t0 (THead k v t)))) (refl_equal T (THead k v t)) (\lambda (t0: T).(\lambda
26 (t1: TList).(\lambda (H: (eq T (THeads k (TApp t1 v) t) (THeads k t1 (THead k
27 v t)))).(eq_ind T (THeads k (TApp t1 v) t) (\lambda (t2: T).(eq T (THead k t0
28 (THeads k (TApp t1 v) t)) (THead k t0 t2))) (refl_equal T (THead k t0 (THeads
29 k (TApp t1 v) t))) (THeads k t1 (THead k v t)) H)))) vs)))).
32 \forall (ts1: TList).(\forall (t1: T).(ex2_2 TList T (\lambda (ts2:
33 TList).(\lambda (t2: T).(eq TList (TCons t1 ts1) (TApp ts2 t2)))) (\lambda
34 (ts2: TList).(\lambda (_: T).(eq nat (tslen ts1) (tslen ts2))))))
36 \lambda (ts1: TList).(TList_ind (\lambda (t: TList).(\forall (t1: T).(ex2_2
37 TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons t1 t) (TApp
38 ts2 t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (tslen t) (tslen
39 ts2))))))) (\lambda (t1: T).(ex2_2_intro TList T (\lambda (ts2:
40 TList).(\lambda (t2: T).(eq TList (TCons t1 TNil) (TApp ts2 t2)))) (\lambda
41 (ts2: TList).(\lambda (_: T).(eq nat O (tslen ts2)))) TNil t1 (refl_equal
42 TList (TApp TNil t1)) (refl_equal nat (tslen TNil)))) (\lambda (t:
43 T).(\lambda (t0: TList).(\lambda (H: ((\forall (t1: T).(ex2_2 TList T
44 (\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons t1 t0) (TApp ts2
45 t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (tslen t0) (tslen
46 ts2)))))))).(\lambda (t1: T).(let H_x \def (H t) in (let H0 \def H_x in
47 (ex2_2_ind TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons t
48 t0) (TApp ts2 t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (tslen t0)
49 (tslen ts2)))) (ex2_2 TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq
50 TList (TCons t1 (TCons t t0)) (TApp ts2 t2)))) (\lambda (ts2: TList).(\lambda
51 (_: T).(eq nat (S (tslen t0)) (tslen ts2))))) (\lambda (x0: TList).(\lambda
52 (x1: T).(\lambda (H1: (eq TList (TCons t t0) (TApp x0 x1))).(\lambda (H2: (eq
53 nat (tslen t0) (tslen x0))).(eq_ind_r TList (TApp x0 x1) (\lambda (t2:
54 TList).(ex2_2 TList T (\lambda (ts2: TList).(\lambda (t3: T).(eq TList (TCons
55 t1 t2) (TApp ts2 t3)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (S
56 (tslen t0)) (tslen ts2)))))) (eq_ind_r nat (tslen x0) (\lambda (n:
57 nat).(ex2_2 TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons
58 t1 (TApp x0 x1)) (TApp ts2 t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq
59 nat (S n) (tslen ts2)))))) (ex2_2_intro TList T (\lambda (ts2:
60 TList).(\lambda (t2: T).(eq TList (TCons t1 (TApp x0 x1)) (TApp ts2 t2))))
61 (\lambda (ts2: TList).(\lambda (_: T).(eq nat (S (tslen x0)) (tslen ts2))))
62 (TCons t1 x0) x1 (refl_equal TList (TApp (TCons t1 x0) x1)) (refl_equal nat
63 (tslen (TCons t1 x0)))) (tslen t0) H2) (TCons t t0) H1))))) H0))))))) ts1).