update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/C/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/C/fwd.ma
index 37410a7783a8fa3519b117025873812676ab091a..43d43fc7144563dd3d2d59b9aba809cd46301cf6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/C/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/C/fwd.ma
@@ -16,20 +16,19 @@
 
 include "basic_1/C/defs.ma".
 
-let rec C_rect (P: (C \to Type[0])) (f: (\forall (n: nat).(P (CSort n)))) 
-(f0: (\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CHead c k 
-t))))))) (c: C) on c: P c \def match c with [(CSort n) \Rightarrow (f n) | 
-(CHead c0 k t) \Rightarrow (let TMP_1 \def ((C_rect P f f0) c0) in (f0 c0 
-TMP_1 k t))].
+implied rec lemma C_rect (P: (C \to Type[0])) (f: (\forall (n: nat).(P (CSort 
+n)))) (f0: (\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P 
+(CHead c k t))))))) (c: C) on c: P c \def match c with [(CSort n) \Rightarrow 
+(f n) | (CHead c0 k t) \Rightarrow (f0 c0 ((C_rect P f f0) c0) k t)].
 
-theorem C_ind:
+implied lemma C_ind:
  \forall (P: ((C \to Prop))).(((\forall (n: nat).(P (CSort n)))) \to 
 (((\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CHead c k 
 t))))))) \to (\forall (c: C).(P c))))
 \def
  \lambda (P: ((C \to Prop))).(C_rect P).
 
-theorem clt_wf__q_ind:
+fact clt_wf__q_ind:
  \forall (P: ((C \to Prop))).(((\forall (n: nat).((\lambda (P0: ((C \to 
 Prop))).(\lambda (n0: nat).(\forall (c: C).((eq nat (cweight c) n0) \to (P0 
 c))))) P n))) \to (\forall (c: C).(P c)))
@@ -37,28 +36,23 @@ c))))) P n))) \to (\forall (c: C).(P c)))
  let Q \def (\lambda (P: ((C \to Prop))).(\lambda (n: nat).(\forall (c: 
 C).((eq nat (cweight c) n) \to (P c))))) in (\lambda (P: ((C \to 
 Prop))).(\lambda (H: ((\forall (n: nat).(\forall (c: C).((eq nat (cweight c) 
-n) \to (P c)))))).(\lambda (c: C).(let TMP_1 \def (cweight c) in (let TMP_2 
-\def (cweight c) in (let TMP_3 \def (refl_equal nat TMP_2) in (H TMP_1 c 
-TMP_3))))))).
+n) \to (P c)))))).(\lambda (c: C).(H (cweight c) c (refl_equal nat (cweight 
+c)))))).
 
-theorem clt_wf_ind:
+lemma clt_wf_ind:
  \forall (P: ((C \to Prop))).(((\forall (c: C).(((\forall (d: C).((clt d c) 
 \to (P d)))) \to (P c)))) \to (\forall (c: C).(P c)))
 \def
  let Q \def (\lambda (P: ((C \to Prop))).(\lambda (n: nat).(\forall (c: 
 C).((eq nat (cweight c) n) \to (P c))))) in (\lambda (P: ((C \to 
 Prop))).(\lambda (H: ((\forall (c: C).(((\forall (d: C).((lt (cweight d) 
-(cweight c)) \to (P d)))) \to (P c))))).(\lambda (c: C).(let TMP_1 \def 
-(\lambda (c0: C).(P c0)) in (let TMP_11 \def (\lambda (n: nat).(let TMP_2 
-\def (\lambda (c0: C).(P c0)) 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 (c0: C).(P c0)) m))))).(\lambda (c0: C).(\lambda (H1: (eq nat 
-(cweight c0) n0)).(let TMP_4 \def (\lambda (n1: nat).(\forall (m: nat).((lt m 
-n1) \to (\forall (c1: C).((eq nat (cweight c1) m) \to (P c1)))))) in (let 
-TMP_5 \def (cweight c0) in (let H2 \def (eq_ind_r nat n0 TMP_4 H0 TMP_5 H1) 
-in (let TMP_9 \def (\lambda (d: C).(\lambda (H3: (lt (cweight d) (cweight 
-c0))).(let TMP_6 \def (cweight d) in (let TMP_7 \def (cweight d) in (let 
-TMP_8 \def (refl_equal nat TMP_7) in (H2 TMP_6 H3 d TMP_8)))))) in (H c0 
-TMP_9))))))))) in (lt_wf_ind n TMP_3 TMP_10))))) in (clt_wf__q_ind TMP_1 
-TMP_11 c)))))).
+(cweight c)) \to (P d)))) \to (P c))))).(\lambda (c: C).(clt_wf__q_ind 
+(\lambda (c0: C).(P c0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (c0: 
+C).(P c0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) 
+\to (Q (\lambda (c0: C).(P c0)) m))))).(\lambda (c0: C).(\lambda (H1: (eq nat 
+(cweight c0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall 
+(m: nat).((lt m n1) \to (\forall (c1: C).((eq nat (cweight c1) m) \to (P 
+c1)))))) H0 (cweight c0) H1) in (H c0 (\lambda (d: C).(\lambda (H3: (lt 
+(cweight d) (cweight c0))).(H2 (cweight d) H3 d (refl_equal nat (cweight 
+d))))))))))))) c)))).