update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csubst1 / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubst1/props.ma b/matita/matita/contribs/lambdadelta/basic_1/csubst1/props.ma
index 30200e34b8860c696451a209df843d7b4ce01874..349485a88c5d45a45d25e98e126852c4a89ebccd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubst1/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubst1/props.ma
@@ -24,32 +24,20 @@ theorem csubst1_head:
 v c1 c2) \to (csubst1 (s k i) v (CHead c1 k u1) (CHead c2 k u2))))))))))
 \def
  \lambda (k: K).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda 
-(u2: T).(\lambda (H: (subst1 i v u1 u2)).(let TMP_4 \def (\lambda (t: 
-T).(\forall (c1: C).(\forall (c2: C).((csubst1 i v c1 c2) \to (let TMP_1 \def 
-(s k i) in (let TMP_2 \def (CHead c1 k u1) in (let TMP_3 \def (CHead c2 k t) 
-in (csubst1 TMP_1 v TMP_2 TMP_3)))))))) in (let TMP_17 \def (\lambda (c1: 
-C).(\lambda (c2: C).(\lambda (H0: (csubst1 i v c1 c2)).(let TMP_8 \def 
-(\lambda (c: C).(let TMP_5 \def (s k i) in (let TMP_6 \def (CHead c1 k u1) in 
-(let TMP_7 \def (CHead c k u1) in (csubst1 TMP_5 v TMP_6 TMP_7))))) in (let 
-TMP_9 \def (s k i) in (let TMP_10 \def (CHead c1 k u1) in (let TMP_11 \def 
-(csubst1_refl TMP_9 v TMP_10) in (let TMP_16 \def (\lambda (c3: C).(\lambda 
-(H1: (csubst0 i v c1 c3)).(let TMP_12 \def (s k i) in (let TMP_13 \def (CHead 
-c1 k u1) in (let TMP_14 \def (CHead c3 k u1) in (let TMP_15 \def (csubst0_fst 
-k i c1 c3 v H1 u1) in (csubst1_sing TMP_12 v TMP_13 TMP_14 TMP_15))))))) in 
-(csubst1_ind i v c1 TMP_8 TMP_11 TMP_16 c2 H0))))))))) in (let TMP_32 \def 
-(\lambda (t2: T).(\lambda (H0: (subst0 i v u1 t2)).(\lambda (c1: C).(\lambda 
-(c2: C).(\lambda (H1: (csubst1 i v c1 c2)).(let TMP_21 \def (\lambda (c: 
-C).(let TMP_18 \def (s k i) in (let TMP_19 \def (CHead c1 k u1) in (let 
-TMP_20 \def (CHead c k t2) in (csubst1 TMP_18 v TMP_19 TMP_20))))) in (let 
-TMP_22 \def (s k i) in (let TMP_23 \def (CHead c1 k u1) in (let TMP_24 \def 
-(CHead c1 k t2) in (let TMP_25 \def (csubst0_snd k i v u1 t2 H0 c1) in (let 
-TMP_26 \def (csubst1_sing TMP_22 v TMP_23 TMP_24 TMP_25) in (let TMP_31 \def 
-(\lambda (c3: C).(\lambda (H2: (csubst0 i v c1 c3)).(let TMP_27 \def (s k i) 
-in (let TMP_28 \def (CHead c1 k u1) in (let TMP_29 \def (CHead c3 k t2) in 
-(let TMP_30 \def (csubst0_both k i v u1 t2 H0 c1 c3 H2) in (csubst1_sing 
-TMP_27 v TMP_28 TMP_29 TMP_30))))))) in (csubst1_ind i v c1 TMP_21 TMP_26 
-TMP_31 c2 H1))))))))))))) in (subst1_ind i v u1 TMP_4 TMP_17 TMP_32 u2 
-H))))))))).
+(u2: T).(\lambda (H: (subst1 i v u1 u2)).(subst1_ind i v u1 (\lambda (t: 
+T).(\forall (c1: C).(\forall (c2: C).((csubst1 i v c1 c2) \to (csubst1 (s k 
+i) v (CHead c1 k u1) (CHead c2 k t)))))) (\lambda (c1: C).(\lambda (c2: 
+C).(\lambda (H0: (csubst1 i v c1 c2)).(csubst1_ind i v c1 (\lambda (c: 
+C).(csubst1 (s k i) v (CHead c1 k u1) (CHead c k u1))) (csubst1_refl (s k i) 
+v (CHead c1 k u1)) (\lambda (c3: C).(\lambda (H1: (csubst0 i v c1 
+c3)).(csubst1_sing (s k i) v (CHead c1 k u1) (CHead c3 k u1) (csubst0_fst k i 
+c1 c3 v H1 u1)))) c2 H0)))) (\lambda (t2: T).(\lambda (H0: (subst0 i v u1 
+t2)).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csubst1 i v c1 
+c2)).(csubst1_ind i v c1 (\lambda (c: C).(csubst1 (s k i) v (CHead c1 k u1) 
+(CHead c k t2))) (csubst1_sing (s k i) v (CHead c1 k u1) (CHead c1 k t2) 
+(csubst0_snd k i v u1 t2 H0 c1)) (\lambda (c3: C).(\lambda (H2: (csubst0 i v 
+c1 c3)).(csubst1_sing (s k i) v (CHead c1 k u1) (CHead c3 k t2) (csubst0_both 
+k i v u1 t2 H0 c1 c3 H2)))) c2 H1)))))) u2 H)))))).
 
 theorem csubst1_bind:
  \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall 
@@ -59,14 +47,10 @@ u2))))))))))
 \def
  \lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda 
 (u2: T).(\lambda (H: (subst1 i v u1 u2)).(\lambda (c1: C).(\lambda (c2: 
-C).(\lambda (H0: (csubst1 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 (csubst1 n v TMP_4 TMP_6)))))) in (let 
-TMP_8 \def (Bind b) in (let TMP_9 \def (csubst1_head 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: (csubst1 i v c1 c2)).(eq_ind nat (s (Bind b) i) (\lambda (n: 
+nat).(csubst1 n v (CHead c1 (Bind b) u1) (CHead c2 (Bind b) u2))) 
+(csubst1_head (Bind b) i v u1 u2 H c1 c2 H0) (S i) (refl_equal nat (S 
+i))))))))))).
 
 theorem csubst1_flat:
  \forall (f: F).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall 
@@ -76,11 +60,7 @@ u2))))))))))
 \def
  \lambda (f: F).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda 
 (u2: T).(\lambda (H: (subst1 i v u1 u2)).(\lambda (c1: C).(\lambda (c2: 
-C).(\lambda (H0: (csubst1 i v c1 c2)).(let TMP_1 \def (Flat f) in (let TMP_2 
-\def (s TMP_1 i) in (let TMP_7 \def (\lambda (n: nat).(let TMP_3 \def (Flat 
-f) in (let TMP_4 \def (CHead c1 TMP_3 u1) in (let TMP_5 \def (Flat f) in (let 
-TMP_6 \def (CHead c2 TMP_5 u2) in (csubst1 n v TMP_4 TMP_6)))))) in (let 
-TMP_8 \def (Flat f) in (let TMP_9 \def (csubst1_head TMP_8 i v u1 u2 H c1 c2 
-H0) in (let TMP_10 \def (refl_equal nat i) in (eq_ind nat TMP_2 TMP_7 TMP_9 i 
-TMP_10))))))))))))))).
+C).(\lambda (H0: (csubst1 i v c1 c2)).(eq_ind nat (s (Flat f) i) (\lambda (n: 
+nat).(csubst1 n v (CHead c1 (Flat f) u1) (CHead c2 (Flat f) u2))) 
+(csubst1_head (Flat f) i v u1 u2 H c1 c2 H0) i (refl_equal nat i)))))))))).