components C r flt app lift

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/flt/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/flt/fwd.ma
new file mode 100644 (file)
index 0000000..b5bf9f8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_1/flt/fwd.ma
@@ -0,0 +1,53 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/flt/defs.ma".
+
+theorem flt_wf__q_ind:
+ \forall (P: ((C \to (T \to Prop)))).(((\forall (n: nat).((\lambda (P0: ((C 
+\to (T \to Prop)))).(\lambda (n0: nat).(\forall (c: C).(\forall (t: T).((eq 
+nat (fweight c t) n0) \to (P0 c t)))))) P n))) \to (\forall (c: C).(\forall 
+(t: T).(P c t))))
+\def
+ let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall 
+(c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda 
+(P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (n: nat).(\forall (c: 
+C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t))))))).(\lambda (c: 
+C).(\lambda (t: T).(let TMP_1 \def (fweight c t) in (let TMP_2 \def (fweight 
+c t) in (let TMP_3 \def (refl_equal nat TMP_2) in (H TMP_1 c t TMP_3)))))))).
+
+theorem flt_wf_ind:
+ \forall (P: ((C \to (T \to Prop)))).(((\forall (c2: C).(\forall (t2: 
+T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1))))) 
+\to (P c2 t2))))) \to (\forall (c: C).(\forall (t: T).(P c t))))
+\def
+ let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall 
+(c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda 
+(P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (c2: C).(\forall (t2: 
+T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1))))) 
+\to (P c2 t2)))))).(\lambda (c: C).(\lambda (t: T).(let TMP_9 \def (\lambda 
+(n: nat).(let TMP_1 \def (Q P) in (let TMP_8 \def (\lambda (n0: nat).(\lambda 
+(H0: ((\forall (m: nat).((lt m n0) \to (Q P m))))).(\lambda (c0: C).(\lambda 
+(t0: T).(\lambda (H1: (eq nat (fweight c0 t0) n0)).(let TMP_2 \def (\lambda 
+(n1: nat).(\forall (m: nat).((lt m n1) \to (\forall (c1: C).(\forall (t1: 
+T).((eq nat (fweight c1 t1) m) \to (P c1 t1))))))) in (let TMP_3 \def 
+(fweight c0 t0) in (let H2 \def (eq_ind_r nat n0 TMP_2 H0 TMP_3 H1) in (let 
+TMP_7 \def (\lambda (c1: C).(\lambda (t1: T).(\lambda (H3: (flt c1 t1 c0 
+t0)).(let TMP_4 \def (fweight c1 t1) in (let TMP_5 \def (fweight c1 t1) in 
+(let TMP_6 \def (refl_equal nat TMP_5) in (H2 TMP_4 H3 c1 t1 TMP_6))))))) in 
+(H c0 t0 TMP_7)))))))))) in (lt_wf_ind n TMP_1 TMP_8)))) in (flt_wf__q_ind P 
+TMP_9 c t)))))).
+