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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/tlt/defs.ma".
19 theorem tlt_wf__q_ind:
20 \forall (P: ((T \to Prop))).(((\forall (n: nat).((\lambda (P0: ((T \to
21 Prop))).(\lambda (n0: nat).(\forall (t: T).((eq nat (weight t) n0) \to (P0
22 t))))) P n))) \to (\forall (t: T).(P t)))
24 let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t:
25 T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to
26 Prop))).(\lambda (H: ((\forall (n: nat).(\forall (t: T).((eq nat (weight t)
27 n) \to (P t)))))).(\lambda (t: T).(let TMP_1 \def (weight t) in (let TMP_2
28 \def (weight t) in (let TMP_3 \def (refl_equal nat TMP_2) in (H TMP_1 t
32 \forall (P: ((T \to Prop))).(((\forall (t: T).(((\forall (v: T).((tlt v t)
33 \to (P v)))) \to (P t)))) \to (\forall (t: T).(P t)))
35 let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t:
36 T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to
37 Prop))).(\lambda (H: ((\forall (t: T).(((\forall (v: T).((lt (weight v)
38 (weight t)) \to (P v)))) \to (P t))))).(\lambda (t: T).(let TMP_1 \def
39 (\lambda (t0: T).(P t0)) in (let TMP_11 \def (\lambda (n: nat).(let TMP_2
40 \def (\lambda (t0: T).(P t0)) in (let TMP_3 \def (Q TMP_2) in (let TMP_10
41 \def (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) \to (Q
42 (\lambda (t0: T).(P t0)) m))))).(\lambda (t0: T).(\lambda (H1: (eq nat
43 (weight t0) n0)).(let TMP_4 \def (\lambda (n1: nat).(\forall (m: nat).((lt m
44 n1) \to (\forall (t1: T).((eq nat (weight t1) m) \to (P t1)))))) in (let
45 TMP_5 \def (weight t0) in (let H2 \def (eq_ind_r nat n0 TMP_4 H0 TMP_5 H1) in
46 (let TMP_9 \def (\lambda (v: T).(\lambda (H3: (lt (weight v) (weight
47 t0))).(let TMP_6 \def (weight v) in (let TMP_7 \def (weight v) in (let TMP_8
48 \def (refl_equal nat TMP_7) in (H2 TMP_6 H3 v TMP_8)))))) in (H t0
49 TMP_9))))))))) in (lt_wf_ind n TMP_3 TMP_10))))) in (tlt_wf__q_ind TMP_1