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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/C/defs.ma".
19 let rec C_rect (P: (C \to Type[0])) (f: (\forall (n: nat).(P (CSort n))))
20 (f0: (\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CHead c k
21 t))))))) (c: C) on c: P c \def match c with [(CSort n) \Rightarrow (f n) |
22 (CHead c0 k t) \Rightarrow (f0 c0 ((C_rect P f f0) c0) k t)].
25 \forall (P: ((C \to Prop))).(((\forall (n: nat).(P (CSort n)))) \to
26 (((\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CHead c k
27 t))))))) \to (\forall (c: C).(P c))))
29 \lambda (P: ((C \to Prop))).(C_rect P).
31 theorem clt_wf__q_ind:
32 \forall (P: ((C \to Prop))).(((\forall (n: nat).((\lambda (P0: ((C \to
33 Prop))).(\lambda (n0: nat).(\forall (c: C).((eq nat (cweight c) n0) \to (P0
34 c))))) P n))) \to (\forall (c: C).(P c)))
36 let Q \def (\lambda (P: ((C \to Prop))).(\lambda (n: nat).(\forall (c:
37 C).((eq nat (cweight c) n) \to (P c))))) in (\lambda (P: ((C \to
38 Prop))).(\lambda (H: ((\forall (n: nat).(\forall (c: C).((eq nat (cweight c)
39 n) \to (P c)))))).(\lambda (c: C).(H (cweight c) c (refl_equal nat (cweight
43 \forall (P: ((C \to Prop))).(((\forall (c: C).(((\forall (d: C).((clt d c)
44 \to (P d)))) \to (P c)))) \to (\forall (c: C).(P c)))
46 let Q \def (\lambda (P: ((C \to Prop))).(\lambda (n: nat).(\forall (c:
47 C).((eq nat (cweight c) n) \to (P c))))) in (\lambda (P: ((C \to
48 Prop))).(\lambda (H: ((\forall (c: C).(((\forall (d: C).((lt (cweight d)
49 (cweight c)) \to (P d)))) \to (P c))))).(\lambda (c: C).(clt_wf__q_ind
50 (\lambda (c0: C).(P c0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (c0:
51 C).(P c0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0)
52 \to (Q (\lambda (c0: C).(P c0)) m))))).(\lambda (c0: C).(\lambda (H1: (eq nat
53 (cweight c0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall
54 (m: nat).((lt m n1) \to (\forall (c1: C).((eq nat (cweight c1) m) \to (P
55 c1)))))) H0 (cweight c0) H1) in (H c0 (\lambda (d: C).(\lambda (H3: (lt
56 (cweight d) (cweight c0))).(H2 (cweight d) H3 d (refl_equal nat (cweight