update in lambdadelta

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1A/llt/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1A/llt/fwd.ma
new file mode 100644 (file)
index 0000000..65e029b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_1A/llt/fwd.ma
@@ -0,0 +1,46 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/llt/defs.ma".
+
+fact 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).(H (lweight a) a (refl_equal nat (lweight 
+a)))))).
+
+lemma 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).(llt_wf__q_ind 
+(\lambda (a0: A).(P a0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (a0: 
+A).(P a0))) (\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 H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall 
+(m: nat).((lt m n1) \to (\forall (a1: A).((eq nat (lweight a1) m) \to (P 
+a1)))))) H0 (lweight a0) H1) in (H a0 (\lambda (a1: A).(\lambda (H3: (lt 
+(lweight a1) (lweight a0))).(H2 (lweight a1) H3 a1 (refl_equal nat (lweight 
+a1))))))))))))) a)))).
+