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/tlt/defs.ma".
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).(H (weight t) t (refl_equal nat (weight
31 \forall (P: ((T \to Prop))).(((\forall (t: T).(((\forall (v: T).((tlt v t)
32 \to (P v)))) \to (P t)))) \to (\forall (t: T).(P t)))
34 let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t:
35 T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to
36 Prop))).(\lambda (H: ((\forall (t: T).(((\forall (v: T).((lt (weight v)
37 (weight t)) \to (P v)))) \to (P t))))).(\lambda (t: T).(tlt_wf__q_ind
38 (\lambda (t0: T).(P t0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (t0:
39 T).(P t0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0)
40 \to (Q (\lambda (t0: T).(P t0)) m))))).(\lambda (t0: T).(\lambda (H1: (eq nat
41 (weight t0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall
42 (m: nat).((lt m n1) \to (\forall (t1: T).((eq nat (weight t1) m) \to (P
43 t1)))))) H0 (weight t0) H1) in (H t0 (\lambda (v: T).(\lambda (H3: (lt
44 (weight v) (weight t0))).(H2 (weight v) H3 v (refl_equal nat (weight