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/tlist/props.ma".
19 theorem tslt_wf__q_ind:
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).(let TMP_1 \def (tslen ts) in
28 (let TMP_2 \def (tslen ts) in (let TMP_3 \def (refl_equal nat TMP_2) in (H
29 TMP_1 ts TMP_3))))))).
32 \forall (P: ((TList \to Prop))).(((\forall (ts2: TList).(((\forall (ts1:
33 TList).((tslt ts1 ts2) \to (P ts1)))) \to (P ts2)))) \to (\forall (ts:
36 let Q \def (\lambda (P: ((TList \to Prop))).(\lambda (n: nat).(\forall (ts:
37 TList).((eq nat (tslen ts) n) \to (P ts))))) in (\lambda (P: ((TList \to
38 Prop))).(\lambda (H: ((\forall (ts2: TList).(((\forall (ts1: TList).((lt
39 (tslen ts1) (tslen ts2)) \to (P ts1)))) \to (P ts2))))).(\lambda (ts:
40 TList).(let TMP_1 \def (\lambda (t: TList).(P t)) in (let TMP_11 \def
41 (\lambda (n: nat).(let TMP_2 \def (\lambda (t: TList).(P t)) in (let TMP_3
42 \def (Q TMP_2) in (let TMP_10 \def (\lambda (n0: nat).(\lambda (H0: ((\forall
43 (m: nat).((lt m n0) \to (Q (\lambda (t: TList).(P t)) m))))).(\lambda (ts0:
44 TList).(\lambda (H1: (eq nat (tslen ts0) n0)).(let TMP_4 \def (\lambda (n1:
45 nat).(\forall (m: nat).((lt m n1) \to (\forall (ts1: TList).((eq nat (tslen
46 ts1) m) \to (P ts1)))))) in (let TMP_5 \def (tslen ts0) in (let H2 \def
47 (eq_ind_r nat n0 TMP_4 H0 TMP_5 H1) in (let TMP_9 \def (\lambda (ts1:
48 TList).(\lambda (H3: (lt (tslen ts1) (tslen ts0))).(let TMP_6 \def (tslen
49 ts1) in (let TMP_7 \def (tslen ts1) in (let TMP_8 \def (refl_equal nat TMP_7)
50 in (H2 TMP_6 H3 ts1 TMP_8)))))) in (H ts0 TMP_9))))))))) in (lt_wf_ind n
51 TMP_3 TMP_10))))) in (tslt_wf__q_ind TMP_1 TMP_11 ts)))))).
53 theorem tlist_ind_rev:
54 \forall (P: ((TList \to Prop))).((P TNil) \to (((\forall (ts:
55 TList).(\forall (t: T).((P ts) \to (P (TApp ts t)))))) \to (\forall (ts:
58 \lambda (P: ((TList \to Prop))).(\lambda (H: (P TNil)).(\lambda (H0:
59 ((\forall (ts: TList).(\forall (t: T).((P ts) \to (P (TApp ts
60 t))))))).(\lambda (ts: TList).(let TMP_1 \def (\lambda (t: TList).(P t)) in
61 (let TMP_28 \def (\lambda (ts2: TList).(let TMP_2 \def (\lambda (t:
62 TList).(((\forall (ts1: TList).((tslt ts1 t) \to (P ts1)))) \to (P t))) in
63 (let TMP_3 \def (\lambda (_: ((\forall (ts1: TList).((tslt ts1 TNil) \to (P
64 ts1))))).H) in (let TMP_27 \def (\lambda (t: T).(\lambda (t0: TList).(\lambda
65 (_: ((((\forall (ts1: TList).((tslt ts1 t0) \to (P ts1)))) \to (P
66 t0)))).(\lambda (H2: ((\forall (ts1: TList).((tslt ts1 (TCons t t0)) \to (P
67 ts1))))).(let H_x \def (tcons_tapp_ex t0 t) in (let H3 \def H_x in (let TMP_6
68 \def (\lambda (ts3: TList).(\lambda (t2: T).(let TMP_4 \def (TCons t t0) in
69 (let TMP_5 \def (TApp ts3 t2) in (eq TList TMP_4 TMP_5))))) in (let TMP_9
70 \def (\lambda (ts3: TList).(\lambda (_: T).(let TMP_7 \def (tslen t0) in (let
71 TMP_8 \def (tslen ts3) in (eq nat TMP_7 TMP_8))))) in (let TMP_10 \def (TCons
72 t t0) in (let TMP_11 \def (P TMP_10) in (let TMP_26 \def (\lambda (x0:
73 TList).(\lambda (x1: T).(\lambda (H4: (eq TList (TCons t t0) (TApp x0
74 x1))).(\lambda (H5: (eq nat (tslen t0) (tslen x0))).(let TMP_12 \def (TApp x0
75 x1) in (let TMP_13 \def (\lambda (t1: TList).(P t1)) in (let TMP_14 \def
76 (tslen t0) in (let TMP_17 \def (\lambda (n: nat).(let TMP_15 \def (TCons t
77 t0) in (let TMP_16 \def (tslen TMP_15) in (lt n TMP_16)))) in (let TMP_18
78 \def (TCons t t0) in (let TMP_19 \def (tslen TMP_18) in (let TMP_20 \def
79 (le_n TMP_19) in (let TMP_21 \def (tslen x0) in (let TMP_22 \def (eq_ind nat
80 TMP_14 TMP_17 TMP_20 TMP_21 H5) in (let TMP_23 \def (H2 x0 TMP_22) in (let
81 TMP_24 \def (H0 x0 x1 TMP_23) in (let TMP_25 \def (TCons t t0) in (eq_ind_r
82 TList TMP_12 TMP_13 TMP_24 TMP_25 H4))))))))))))))))) in (ex2_2_ind TList T
83 TMP_6 TMP_9 TMP_11 TMP_26 H3)))))))))))) in (TList_ind TMP_2 TMP_3 TMP_27
84 ts2))))) in (tslt_wf_ind TMP_1 TMP_28 ts)))))).