update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_1A / C / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1A/C/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1A/C/fwd.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "basic_1A/C/defs.ma".
+
+implied rec lemma C_rect (P: (C \to Type[0])) (f: (\forall (n: nat).(P (CSort 
+n)))) (f0: (\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P 
+(CHead c k t))))))) (c: C) on c: P c \def match c with [(CSort n) \Rightarrow 
+(f n) | (CHead c0 k t) \Rightarrow (f0 c0 ((C_rect P f f0) c0) k t)].
+
+implied lemma C_ind:
+ \forall (P: ((C \to Prop))).(((\forall (n: nat).(P (CSort n)))) \to 
+(((\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CHead c k 
+t))))))) \to (\forall (c: C).(P c))))
+\def
+ \lambda (P: ((C \to Prop))).(C_rect P).
+
+fact clt_wf__q_ind:
+ \forall (P: ((C \to Prop))).(((\forall (n: nat).((\lambda (P0: ((C \to 
+Prop))).(\lambda (n0: nat).(\forall (c: C).((eq nat (cweight c) n0) \to (P0 
+c))))) P n))) \to (\forall (c: C).(P c)))
+\def
+ let Q \def (\lambda (P: ((C \to Prop))).(\lambda (n: nat).(\forall (c: 
+C).((eq nat (cweight c) n) \to (P c))))) in (\lambda (P: ((C \to 
+Prop))).(\lambda (H: ((\forall (n: nat).(\forall (c: C).((eq nat (cweight c) 
+n) \to (P c)))))).(\lambda (c: C).(H (cweight c) c (refl_equal nat (cweight 
+c)))))).
+
+lemma clt_wf_ind:
+ \forall (P: ((C \to Prop))).(((\forall (c: C).(((\forall (d: C).((clt d c) 
+\to (P d)))) \to (P c)))) \to (\forall (c: C).(P c)))
+\def
+ let Q \def (\lambda (P: ((C \to Prop))).(\lambda (n: nat).(\forall (c: 
+C).((eq nat (cweight c) n) \to (P c))))) in (\lambda (P: ((C \to 
+Prop))).(\lambda (H: ((\forall (c: C).(((\forall (d: C).((lt (cweight d) 
+(cweight c)) \to (P d)))) \to (P c))))).(\lambda (c: C).(clt_wf__q_ind 
+(\lambda (c0: C).(P c0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (c0: 
+C).(P c0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) 
+\to (Q (\lambda (c0: C).(P c0)) m))))).(\lambda (c0: C).(\lambda (H1: (eq nat 
+(cweight c0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall 
+(m: nat).((lt m n1) \to (\forall (c1: C).((eq nat (cweight c1) m) \to (P 
+c1)))))) H0 (cweight c0) H1) in (H c0 (\lambda (d: C).(\lambda (H3: (lt 
+(cweight d) (cweight c0))).(H2 (cweight d) H3 d (refl_equal nat (cweight 
+d))))))))))))) c)))).
+