components: A asucc aplus leq llt aprem ex0

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / llt / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/llt/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/llt/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_1/llt/defs.ma".
+
+theorem llt_wf__q_ind:
+ \forall (P: ((A \to Prop))).(((\forall (n: nat).((\lambda (P0: ((A \to 
+Prop))).(\lambda (n0: nat).(\forall (a: A).((eq nat (lweight a) n0) \to (P0 
+a))))) P n))) \to (\forall (a: A).(P a)))
+\def
+ let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a: 
+A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((A \to 
+Prop))).(\lambda (H: ((\forall (n: nat).(\forall (a: A).((eq nat (lweight a) 
+n) \to (P a)))))).(\lambda (a: A).(let TMP_1 \def (lweight a) in (let TMP_2 
+\def (lweight a) in (let TMP_3 \def (refl_equal nat TMP_2) in (H TMP_1 a 
+TMP_3))))))).
+
+theorem llt_wf_ind:
+ \forall (P: ((A \to Prop))).(((\forall (a2: A).(((\forall (a1: A).((llt a1 
+a2) \to (P a1)))) \to (P a2)))) \to (\forall (a: A).(P a)))
+\def
+ let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a: 
+A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((A \to 
+Prop))).(\lambda (H: ((\forall (a2: A).(((\forall (a1: A).((lt (lweight a1) 
+(lweight a2)) \to (P a1)))) \to (P a2))))).(\lambda (a: A).(let TMP_1 \def 
+(\lambda (a0: A).(P a0)) in (let TMP_11 \def (\lambda (n: nat).(let TMP_2 
+\def (\lambda (a0: A).(P a0)) in (let TMP_3 \def (Q TMP_2) in (let TMP_10 
+\def (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) \to (Q 
+(\lambda (a0: A).(P a0)) m))))).(\lambda (a0: A).(\lambda (H1: (eq nat 
+(lweight a0) n0)).(let TMP_4 \def (\lambda (n1: nat).(\forall (m: nat).((lt m 
+n1) \to (\forall (a1: A).((eq nat (lweight a1) m) \to (P a1)))))) in (let 
+TMP_5 \def (lweight a0) in (let H2 \def (eq_ind_r nat n0 TMP_4 H0 TMP_5 H1) 
+in (let TMP_9 \def (\lambda (a1: A).(\lambda (H3: (lt (lweight a1) (lweight 
+a0))).(let TMP_6 \def (lweight a1) in (let TMP_7 \def (lweight a1) in (let 
+TMP_8 \def (refl_equal nat TMP_7) in (H2 TMP_6 H3 a1 TMP_8)))))) in (H a0 
+TMP_9))))))))) in (lt_wf_ind n TMP_3 TMP_10))))) in (llt_wf__q_ind TMP_1 
+TMP_11 a)))))).
+