update in basic_2

[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
index 025bf660fa43d5128b2f891f881d12cced130652..8d45d3775af57733596afec64a06f79a4525a4f4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/llt/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/llt/fwd.ma
@@ -16,7 +16,7 @@
 
 include "basic_1/llt/defs.ma".
 
-theorem llt_wf__q_ind:
+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)))
@@ -24,28 +24,23 @@ a))))) P n))) \to (\forall (a: A).(P a)))
  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))))))).
+n) \to (P a)))))).(\lambda (a: A).(H (lweight a) a (refl_equal nat (lweight 
+a)))))).
 
-theorem llt_wf_ind:
+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).(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)))))).
+(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)))).