update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csubst0 / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubst0/props.ma b/matita/matita/contribs/lambdadelta/basic_1/csubst0/props.ma
index 40f7fd4a78693fef08a33d162b302721079c98b8..bb427a677eb88e1841d59891604160156c6e0638 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubst0/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubst0/props.ma
@@ -16,35 +16,26 @@
 
 include "basic_1/csubst0/defs.ma".
 
-theorem csubst0_snd_bind:
+lemma csubst0_snd_bind:
  \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall 
 (u2: T).((subst0 i v u1 u2) \to (\forall (c: C).(csubst0 (S i) v (CHead c 
 (Bind b) u1) (CHead c (Bind b) u2))))))))
 \def
  \lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda 
-(u2: T).(\lambda (H: (subst0 i v u1 u2)).(\lambda (c: C).(let TMP_1 \def 
-(Bind b) in (let TMP_2 \def (s TMP_1 i) in (let TMP_7 \def (\lambda (n: 
-nat).(let TMP_3 \def (Bind b) in (let TMP_4 \def (CHead c TMP_3 u1) in (let 
-TMP_5 \def (Bind b) in (let TMP_6 \def (CHead c TMP_5 u2) in (csubst0 n v 
-TMP_4 TMP_6)))))) in (let TMP_8 \def (Bind b) in (let TMP_9 \def (csubst0_snd 
-TMP_8 i v u1 u2 H c) in (let TMP_10 \def (S i) in (let TMP_11 \def (S i) in 
-(let TMP_12 \def (refl_equal nat TMP_11) in (eq_ind nat TMP_2 TMP_7 TMP_9 
-TMP_10 TMP_12))))))))))))))).
+(u2: T).(\lambda (H: (subst0 i v u1 u2)).(\lambda (c: C).(eq_ind nat (s (Bind 
+b) i) (\lambda (n: nat).(csubst0 n v (CHead c (Bind b) u1) (CHead c (Bind b) 
+u2))) (csubst0_snd (Bind b) i v u1 u2 H c) (S i) (refl_equal nat (S 
+i))))))))).
 
-theorem csubst0_fst_bind:
+lemma csubst0_fst_bind:
  \forall (b: B).(\forall (i: nat).(\forall (c1: C).(\forall (c2: C).(\forall 
 (v: T).((csubst0 i v c1 c2) \to (\forall (u: T).(csubst0 (S i) v (CHead c1 
 (Bind b) u) (CHead c2 (Bind b) u))))))))
 \def
  \lambda (b: B).(\lambda (i: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda 
-(v: T).(\lambda (H: (csubst0 i v c1 c2)).(\lambda (u: T).(let TMP_1 \def 
-(Bind b) in (let TMP_2 \def (s TMP_1 i) in (let TMP_7 \def (\lambda (n: 
-nat).(let TMP_3 \def (Bind b) in (let TMP_4 \def (CHead c1 TMP_3 u) in (let 
-TMP_5 \def (Bind b) in (let TMP_6 \def (CHead c2 TMP_5 u) in (csubst0 n v 
-TMP_4 TMP_6)))))) in (let TMP_8 \def (Bind b) in (let TMP_9 \def (csubst0_fst 
-TMP_8 i c1 c2 v H u) in (let TMP_10 \def (S i) in (let TMP_11 \def (S i) in 
-(let TMP_12 \def (refl_equal nat TMP_11) in (eq_ind nat TMP_2 TMP_7 TMP_9 
-TMP_10 TMP_12))))))))))))))).
+(v: T).(\lambda (H: (csubst0 i v c1 c2)).(\lambda (u: T).(eq_ind nat (s (Bind 
+b) i) (\lambda (n: nat).(csubst0 n v (CHead c1 (Bind b) u) (CHead c2 (Bind b) 
+u))) (csubst0_fst (Bind b) i c1 c2 v H u) (S i) (refl_equal nat (S i))))))))).
 
 theorem csubst0_both_bind:
  \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall 
@@ -54,12 +45,8 @@ u2))))))))))
 \def
  \lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda 
 (u2: T).(\lambda (H: (subst0 i v u1 u2)).(\lambda (c1: C).(\lambda (c2: 
-C).(\lambda (H0: (csubst0 i v c1 c2)).(let TMP_1 \def (Bind b) in (let TMP_2 
-\def (s TMP_1 i) in (let TMP_7 \def (\lambda (n: nat).(let TMP_3 \def (Bind 
-b) in (let TMP_4 \def (CHead c1 TMP_3 u1) in (let TMP_5 \def (Bind b) in (let 
-TMP_6 \def (CHead c2 TMP_5 u2) in (csubst0 n v TMP_4 TMP_6)))))) in (let 
-TMP_8 \def (Bind b) in (let TMP_9 \def (csubst0_both TMP_8 i v u1 u2 H c1 c2 
-H0) in (let TMP_10 \def (S i) in (let TMP_11 \def (S i) in (let TMP_12 \def 
-(refl_equal nat TMP_11) in (eq_ind nat TMP_2 TMP_7 TMP_9 TMP_10 
-TMP_12))))))))))))))))).
+C).(\lambda (H0: (csubst0 i v c1 c2)).(eq_ind nat (s (Bind b) i) (\lambda (n: 
+nat).(csubst0 n v (CHead c1 (Bind b) u1) (CHead c2 (Bind b) u2))) 
+(csubst0_both (Bind b) i v u1 u2 H c1 c2 H0) (S i) (refl_equal nat (S 
+i))))))))))).