update in basic_2

[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
index b5bf9f87bf3d9e31fe1dc9a0e548608ac8ba1b33..a25e739167fd73ee260734166a89582dada254ad 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/flt/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/flt/fwd.ma
@@ -16,7 +16,7 @@
 
 include "basic_1/flt/defs.ma".
 
-theorem flt_wf__q_ind:
+fact 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 
@@ -26,10 +26,9 @@ nat (fweight c t) n0) \to (P0 c t)))))) P n))) \to (\forall (c: C).(\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)))))))).
+C).(\lambda (t: T).(H (fweight c t) c t (refl_equal nat (fweight c t))))))).
 
-theorem flt_wf_ind:
+lemma 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))))
@@ -38,16 +37,13 @@ T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1)))))
 (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)))))).
+\to (P c2 t2)))))).(\lambda (c: C).(\lambda (t: T).(flt_wf__q_ind P (\lambda 
+(n: nat).(lt_wf_ind n (Q P) (\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 H2 \def (eq_ind_r nat n0 (\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))))))) H0 (fweight c0 t0) H1) in (H c0 t0 
+(\lambda (c1: C).(\lambda (t1: T).(\lambda (H3: (flt c1 t1 c0 t0)).(H2 
+(fweight c1 t1) H3 c1 t1 (refl_equal nat (fweight c1 t1))))))))))))))) c 
+t))))).