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/llt/defs.ma".
20 \forall (P: ((A \to Prop))).(((\forall (n: nat).((\lambda (P0: ((A \to
21 Prop))).(\lambda (n0: nat).(\forall (a: A).((eq nat (lweight a) n0) \to (P0
22 a))))) P n))) \to (\forall (a: A).(P a)))
24 let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a:
25 A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((A \to
26 Prop))).(\lambda (H: ((\forall (n: nat).(\forall (a: A).((eq nat (lweight a)
27 n) \to (P a)))))).(\lambda (a: A).(H (lweight a) a (refl_equal nat (lweight
31 \forall (P: ((A \to Prop))).(((\forall (a2: A).(((\forall (a1: A).((llt a1
32 a2) \to (P a1)))) \to (P a2)))) \to (\forall (a: A).(P a)))
34 let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a:
35 A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((A \to
36 Prop))).(\lambda (H: ((\forall (a2: A).(((\forall (a1: A).((lt (lweight a1)
37 (lweight a2)) \to (P a1)))) \to (P a2))))).(\lambda (a: A).(llt_wf__q_ind
38 (\lambda (a0: A).(P a0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (a0:
39 A).(P a0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0)
40 \to (Q (\lambda (a0: A).(P a0)) m))))).(\lambda (a0: A).(\lambda (H1: (eq nat
41 (lweight a0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall
42 (m: nat).((lt m n1) \to (\forall (a1: A).((eq nat (lweight a1) m) \to (P
43 a1)))))) H0 (lweight a0) H1) in (H a0 (\lambda (a1: A).(\lambda (H3: (lt
44 (lweight a1) (lweight a0))).(H2 (lweight a1) H3 a1 (refl_equal nat (lweight
45 a1))))))))))))) a)))).