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/props.ma".
20 \forall (P: ((TList \to Prop))).(((\forall (n: nat).((\lambda (P0: ((TList
21 \to Prop))).(\lambda (n0: nat).(\forall (ts: TList).((eq nat (tslen ts) n0)
22 \to (P0 ts))))) P n))) \to (\forall (ts: TList).(P ts)))
24 let Q \def (\lambda (P: ((TList \to Prop))).(\lambda (n: nat).(\forall (ts:
25 TList).((eq nat (tslen ts) n) \to (P ts))))) in (\lambda (P: ((TList \to
26 Prop))).(\lambda (H: ((\forall (n: nat).(\forall (ts: TList).((eq nat (tslen
27 ts) n) \to (P ts)))))).(\lambda (ts: TList).(H (tslen ts) ts (refl_equal nat
31 \forall (P: ((TList \to Prop))).(((\forall (ts2: TList).(((\forall (ts1:
32 TList).((tslt ts1 ts2) \to (P ts1)))) \to (P ts2)))) \to (\forall (ts:
35 let Q \def (\lambda (P: ((TList \to Prop))).(\lambda (n: nat).(\forall (ts:
36 TList).((eq nat (tslen ts) n) \to (P ts))))) in (\lambda (P: ((TList \to
37 Prop))).(\lambda (H: ((\forall (ts2: TList).(((\forall (ts1: TList).((lt
38 (tslen ts1) (tslen ts2)) \to (P ts1)))) \to (P ts2))))).(\lambda (ts:
39 TList).(tslt_wf__q_ind (\lambda (t: TList).(P t)) (\lambda (n:
40 nat).(lt_wf_ind n (Q (\lambda (t: TList).(P t))) (\lambda (n0: nat).(\lambda
41 (H0: ((\forall (m: nat).((lt m n0) \to (Q (\lambda (t: TList).(P t))
42 m))))).(\lambda (ts0: TList).(\lambda (H1: (eq nat (tslen ts0) n0)).(let H2
43 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall (m: nat).((lt m n1) \to
44 (\forall (ts1: TList).((eq nat (tslen ts1) m) \to (P ts1)))))) H0 (tslen ts0)
45 H1) in (H ts0 (\lambda (ts1: TList).(\lambda (H3: (lt (tslen ts1) (tslen
46 ts0))).(H2 (tslen ts1) H3 ts1 (refl_equal nat (tslen ts1))))))))))))) ts)))).
49 \forall (P: ((TList \to Prop))).((P TNil) \to (((\forall (ts:
50 TList).(\forall (t: T).((P ts) \to (P (TApp ts t)))))) \to (\forall (ts:
53 \lambda (P: ((TList \to Prop))).(\lambda (H: (P TNil)).(\lambda (H0:
54 ((\forall (ts: TList).(\forall (t: T).((P ts) \to (P (TApp ts
55 t))))))).(\lambda (ts: TList).(tslt_wf_ind (\lambda (t: TList).(P t))
56 (\lambda (ts2: TList).(TList_ind (\lambda (t: TList).(((\forall (ts1:
57 TList).((tslt ts1 t) \to (P ts1)))) \to (P t))) (\lambda (_: ((\forall (ts1:
58 TList).((tslt ts1 TNil) \to (P ts1))))).H) (\lambda (t: T).(\lambda (t0:
59 TList).(\lambda (_: ((((\forall (ts1: TList).((tslt ts1 t0) \to (P ts1))))
60 \to (P t0)))).(\lambda (H2: ((\forall (ts1: TList).((tslt ts1 (TCons t t0))
61 \to (P ts1))))).(let H_x \def (tcons_tapp_ex t0 t) in (let H3 \def H_x in
62 (ex2_2_ind TList T (\lambda (ts3: TList).(\lambda (t2: T).(eq TList (TCons t
63 t0) (TApp ts3 t2)))) (\lambda (ts3: TList).(\lambda (_: T).(eq nat (tslen t0)
64 (tslen ts3)))) (P (TCons t t0)) (\lambda (x0: TList).(\lambda (x1:
65 T).(\lambda (H4: (eq TList (TCons t t0) (TApp x0 x1))).(\lambda (H5: (eq nat
66 (tslen t0) (tslen x0))).(eq_ind_r TList (TApp x0 x1) (\lambda (t1: TList).(P
67 t1)) (H0 x0 x1 (H2 x0 (eq_ind nat (tslen t0) (\lambda (n: nat).(lt n (tslen
68 (TCons t t0)))) (le_n (tslen (TCons t t0))) (tslen x0) H5))) (TCons t t0)
69 H4))))) H3))))))) ts2)) ts)))).