X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fty3%2Fsubst1.ma;h=43a6d483c3df8d1d37d6155f4813385abd1980a0;hb=57ae1762497a5f3ea75740e2908e04adb8642cc2;hp=ca9516e589b7b1080fb9416827fe5d052088f7e8;hpb=88a68a9c334646bc17314d5327cd3b790202acd6;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/ty3/subst1.ma b/matita/matita/contribs/lambdadelta/basic_1/ty3/subst1.ma
index ca9516e58..43a6d483c 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/ty3/subst1.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/ty3/subst1.ma
@@ -14,13 +14,13 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/ty3/props.ma".
+include "basic_1/ty3/props.ma".
 
-include "Basic-1/pc3/subst1.ma".
+include "basic_1/pc3/subst1.ma".
 
-include "Basic-1/getl/getl.ma".
+include "basic_1/getl/getl.ma".
 
-theorem ty3_gen_cabbr:
+lemma ty3_gen_cabbr:
  \forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c 
 t1 t2) \to (\forall (e: C).(\forall (u: T).(\forall (d: nat).((getl d c 
 (CHead e (Bind Abbr) u)) \to (\forall (a0: C).((csubst1 d u c a0) \to 
@@ -102,24 +102,25 @@ O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S n) O t)
 (\lambda (H6: (lt n d0)).(let H7 \def (eq_ind nat (minus d0 n) (\lambda (n0: 
 nat).(getl n0 (CHead d (Bind Abbr) u) (CHead e (Bind Abbr) u0))) 
 (getl_conf_le d0 (CHead e (Bind Abbr) u0) c0 H3 (CHead d (Bind Abbr) u) n H0 
-(le_S_n n d0 (le_S (S n) d0 H6))) (S (minus d0 (S n))) (minus_x_Sy d0 n H6)) 
-in (ex2_ind C (\lambda (e2: C).(csubst1 (minus d0 n) u0 (CHead d (Bind Abbr) 
-u) e2)) (\lambda (e2: C).(getl n a0 e2)) (ex3_2 T T (\lambda (y1: T).(\lambda 
-(_: T).(subst1 d0 u0 (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda 
-(y2: T).(subst1 d0 u0 (lift (S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (x: C).(\lambda (H8: (csubst1 
-(minus d0 n) u0 (CHead d (Bind Abbr) u) x)).(\lambda (H9: (getl n a0 x)).(let 
-H10 \def (eq_ind nat (minus d0 n) (\lambda (n0: nat).(csubst1 n0 u0 (CHead d 
-(Bind Abbr) u) x)) H8 (S (minus d0 (S n))) (minus_x_Sy d0 n H6)) in (let H11 
-\def (csubst1_gen_head (Bind Abbr) d x u u0 (minus d0 (S n)) H10) in 
-(ex3_2_ind T C (\lambda (u2: T).(\lambda (c2: C).(eq C x (CHead c2 (Bind 
-Abbr) u2)))) (\lambda (u2: T).(\lambda (_: C).(subst1 (minus d0 (S n)) u0 u 
-u2))) (\lambda (_: T).(\lambda (c2: C).(csubst1 (minus d0 (S n)) u0 d c2))) 
-(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef n) (lift (S 
-O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S n) O t) 
-(lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) 
-(\lambda (x0: T).(\lambda (x1: C).(\lambda (H12: (eq C x (CHead x1 (Bind 
-Abbr) x0))).(\lambda (H13: (subst1 (minus d0 (S n)) u0 u x0)).(\lambda (H14: 
+(le_S_n n d0 (le_S_n (S n) (S d0) (le_S (S (S n)) (S d0) (le_n_S (S n) d0 
+H6))))) (S (minus d0 (S n))) (minus_x_Sy d0 n H6)) in (ex2_ind C (\lambda 
+(e2: C).(csubst1 (minus d0 n) u0 (CHead d (Bind Abbr) u) e2)) (\lambda (e2: 
+C).(getl n a0 e2)) (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 
+(TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 
+u0 (lift (S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: 
+T).(ty3 g a y1 y2)))) (\lambda (x: C).(\lambda (H8: (csubst1 (minus d0 n) u0 
+(CHead d (Bind Abbr) u) x)).(\lambda (H9: (getl n a0 x)).(let H10 \def 
+(eq_ind nat (minus d0 n) (\lambda (n0: nat).(csubst1 n0 u0 (CHead d (Bind 
+Abbr) u) x)) H8 (S (minus d0 (S n))) (minus_x_Sy d0 n H6)) in (let H11 \def 
+(csubst1_gen_head (Bind Abbr) d x u u0 (minus d0 (S n)) H10) in (ex3_2_ind T 
+C (\lambda (u2: T).(\lambda (c2: C).(eq C x (CHead c2 (Bind Abbr) u2)))) 
+(\lambda (u2: T).(\lambda (_: C).(subst1 (minus d0 (S n)) u0 u u2))) (\lambda 
+(_: T).(\lambda (c2: C).(csubst1 (minus d0 (S n)) u0 d c2))) (ex3_2 T T 
+(\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef n) (lift (S O) d0 
+y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S n) O t) (lift 
+(S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda 
+(x0: T).(\lambda (x1: C).(\lambda (H12: (eq C x (CHead x1 (Bind Abbr) 
+x0))).(\lambda (H13: (subst1 (minus d0 (S n)) u0 u x0)).(\lambda (H14: 
 (csubst1 (minus d0 (S n)) u0 d x1)).(let H15 \def (eq_ind C x (\lambda (c1: 
 C).(getl n a0 c1)) H9 (CHead x1 (Bind Abbr) x0) H12) in (let H16 \def (eq_ind 
 nat d0 (\lambda (n0: nat).(drop (S O) n0 a0 a)) H5 (S (plus n (minus d0 (S 
@@ -180,40 +181,39 @@ T).(subst1 n0 u0 (lift (S n) O t) (lift (S O) n0 y2)))) (\lambda (y1:
 T).(\lambda (y2: T).(ty3 g a y1 y2))))) (let H10 \def (eq_ind C (CHead d 
 (Bind Abbr) u) (\lambda (c1: C).(getl n c0 c1)) H0 (CHead e (Bind Abbr) u0) 
 (getl_mono c0 (CHead d (Bind Abbr) u) n H0 (CHead e (Bind Abbr) u0) H9)) in 
-(let H11 \def (f_equal C C (\lambda (e0: C).(match e0 in C return (\lambda 
-(_: C).C) with [(CSort _) \Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) 
-(CHead d (Bind Abbr) u) (CHead e (Bind Abbr) u0) (getl_mono c0 (CHead d (Bind 
-Abbr) u) n H0 (CHead e (Bind Abbr) u0) H9)) in ((let H12 \def (f_equal C T 
-(\lambda (e0: C).(match e0 in C return (\lambda (_: C).T) with [(CSort _) 
-\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind Abbr) u) 
+(let H11 \def (f_equal C C (\lambda (e0: C).(match e0 with [(CSort _) 
+\Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) (CHead d (Bind Abbr) u) 
 (CHead e (Bind Abbr) u0) (getl_mono c0 (CHead d (Bind Abbr) u) n H0 (CHead e 
-(Bind Abbr) u0) H9)) in (\lambda (H13: (eq C d e)).(let H14 \def (eq_ind_r T 
-u0 (\lambda (t0: T).(getl n c0 (CHead e (Bind Abbr) t0))) H10 u H12) in (let 
-H15 \def (eq_ind_r T u0 (\lambda (t0: T).(csubst1 n t0 c0 a0)) H8 u H12) in 
-(eq_ind T u (\lambda (t0: T).(ex3_2 T T (\lambda (y1: T).(\lambda (_: 
-T).(subst1 n t0 (TLRef n) (lift (S O) n y1)))) (\lambda (_: T).(\lambda (y2: 
-T).(subst1 n t0 (lift (S n) O t) (lift (S O) n y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))))) (let H16 \def (eq_ind_r C e (\lambda 
-(c1: C).(getl n c0 (CHead c1 (Bind Abbr) u))) H14 d H13) in (ex3_2_intro T T 
-(\lambda (y1: T).(\lambda (_: T).(subst1 n u (TLRef n) (lift (S O) n y1)))) 
-(\lambda (_: T).(\lambda (y2: T).(subst1 n u (lift (S n) O t) (lift (S O) n 
-y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) (lift n O u) (lift 
-n O t) (subst1_single n u (TLRef n) (lift (S O) n (lift n O u)) (eq_ind_r T 
-(lift (plus (S O) n) O u) (\lambda (t0: T).(subst0 n u (TLRef n) t0)) 
-(subst0_lref u n) (lift (S O) n (lift n O u)) (lift_free u n (S O) O n (le_n 
-(plus O n)) (le_O_n n)))) (eq_ind_r T (lift (plus (S O) n) O t) (\lambda (t0: 
-T).(subst1 n u (lift (S n) O t) t0)) (subst1_refl n u (lift (S n) O t)) (lift 
-(S O) n (lift n O t)) (lift_free t n (S O) O n (le_n (plus O n)) (le_O_n n))) 
-(ty3_lift g d u t H1 a O n (getl_conf_ge_drop Abbr a0 d u n (csubst1_getl_ge 
-n n (le_n n) c0 a0 u H15 (CHead d (Bind Abbr) u) H16) a H7)))) u0 H12))))) 
-H11))) d0 H6))))) (\lambda (H6: (lt d0 n)).(eq_ind_r nat (S (plus O (minus n 
-(S O)))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: 
+(Bind Abbr) u0) H9)) in ((let H12 \def (f_equal C T (\lambda (e0: C).(match 
+e0 with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d 
+(Bind Abbr) u) (CHead e (Bind Abbr) u0) (getl_mono c0 (CHead d (Bind Abbr) u) 
+n H0 (CHead e (Bind Abbr) u0) H9)) in (\lambda (H13: (eq C d e)).(let H14 
+\def (eq_ind_r T u0 (\lambda (t0: T).(getl n c0 (CHead e (Bind Abbr) t0))) 
+H10 u H12) in (let H15 \def (eq_ind_r T u0 (\lambda (t0: T).(csubst1 n t0 c0 
+a0)) H8 u H12) in (eq_ind T u (\lambda (t0: T).(ex3_2 T T (\lambda (y1: 
+T).(\lambda (_: T).(subst1 n t0 (TLRef n) (lift (S O) n y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(subst1 n t0 (lift (S n) O t) (lift (S O) n y2)))) 
+(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (let H16 \def (eq_ind_r 
+C e (\lambda (c1: C).(getl n c0 (CHead c1 (Bind Abbr) u))) H14 d H13) in 
+(ex3_2_intro T T (\lambda (y1: T).(\lambda (_: T).(subst1 n u (TLRef n) (lift 
+(S O) n y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 n u (lift (S n) O t) 
+(lift (S O) n y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) 
+(lift n O u) (lift n O t) (subst1_single n u (TLRef n) (lift (S O) n (lift n 
+O u)) (eq_ind_r T (lift (plus (S O) n) O u) (\lambda (t0: T).(subst0 n u 
+(TLRef n) t0)) (subst0_lref u n) (lift (S O) n (lift n O u)) (lift_free u n 
+(S O) O n (le_plus_r O n) (le_O_n n)))) (eq_ind_r T (lift (plus (S O) n) O t) 
+(\lambda (t0: T).(subst1 n u (lift (S n) O t) t0)) (subst1_refl n u (lift (S 
+n) O t)) (lift (S O) n (lift n O t)) (lift_free t n (S O) O n (le_plus_r O n) 
+(le_O_n n))) (ty3_lift g d u t H1 a O n (getl_conf_ge_drop Abbr a0 d u n 
+(csubst1_getl_ge n n (le_n n) c0 a0 u H15 (CHead d (Bind Abbr) u) H16) a 
+H7)))) u0 H12))))) H11))) d0 H6))))) (\lambda (H6: (lt d0 n)).(eq_ind_r nat 
+(S (plus O (minus n (S O)))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: 
+T).(\lambda (_: T).(subst1 d0 u0 (TLRef n0) (lift (S O) d0 y1)))) (\lambda 
+(_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S n) O t) (lift (S O) d0 y2)))) 
+(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind nat (plus (S O) 
+(minus n (S O))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: 
 T).(subst1 d0 u0 (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda 
 (y2: T).(subst1 d0 u0 (lift (S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind nat (plus (S O) (minus n (S 
-O))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 
-d0 u0 (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
-T).(subst1 d0 u0 (lift (S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: 
 T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind_r nat (plus (minus n (S O)) 
 (S O)) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 
 d0 u0 (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
@@ -232,30 +232,31 @@ u0 (lift (S n) O t) t0)) (subst1_refl d0 u0 (lift (S n) O t)) (lift (S O) d0
 (plus O n) H6)) (le_O_n d0))) (eq_ind_r nat (S (minus n (S O))) (\lambda (n0: 
 nat).(ty3 g a (TLRef (minus n (S O))) (lift n0 O t))) (ty3_abbr g (minus n (S 
 O)) a d u (getl_drop_conf_ge n (CHead d (Bind Abbr) u) a0 (csubst1_getl_ge d0 
-n (le_S_n d0 n (le_S (S d0) n H6)) c0 a0 u0 H4 (CHead d (Bind Abbr) u) H0) a 
-(S O) d0 H5 (eq_ind_r nat (plus (S O) d0) (\lambda (n0: nat).(le n0 n)) H6 
-(plus d0 (S O)) (plus_sym d0 (S O)))) t H1) n (minus_x_SO n (le_lt_trans O d0 
-n (le_O_n d0) H6)))) (plus (S O) (minus n (S O))) (plus_sym (S O) (minus n (S 
-O)))) (S (plus O (minus n (S O)))) (refl_equal nat (S (plus O (minus n (S 
-O)))))) n (lt_plus_minus O n (le_lt_trans O d0 n (le_O_n d0) 
-H6))))))))))))))))))))) (\lambda (n: nat).(\lambda (c0: C).(\lambda (d: 
-C).(\lambda (u: T).(\lambda (H0: (getl n c0 (CHead d (Bind Abst) 
-u))).(\lambda (t: T).(\lambda (H1: (ty3 g d u t)).(\lambda (H2: ((\forall (e: 
-C).(\forall (u0: T).(\forall (d0: nat).((getl d0 d (CHead e (Bind Abbr) u0)) 
-\to (\forall (a0: C).((csubst1 d0 u0 d a0) \to (\forall (a: C).((drop (S O) 
-d0 a0 a) \to (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 u 
-(lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 t (lift 
-(S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 
-y2)))))))))))))).(\lambda (e: C).(\lambda (u0: T).(\lambda (d0: nat).(\lambda 
-(H3: (getl d0 c0 (CHead e (Bind Abbr) u0))).(\lambda (a0: C).(\lambda (H4: 
-(csubst1 d0 u0 c0 a0)).(\lambda (a: C).(\lambda (H5: (drop (S O) d0 a0 
-a)).(lt_eq_gt_e n d0 (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 
-u0 (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 
-d0 u0 (lift (S n) O u) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: 
-T).(ty3 g a y1 y2)))) (\lambda (H6: (lt n d0)).(let H7 \def (eq_ind nat 
-(minus d0 n) (\lambda (n0: nat).(getl n0 (CHead d (Bind Abst) u) (CHead e 
-(Bind Abbr) u0))) (getl_conf_le d0 (CHead e (Bind Abbr) u0) c0 H3 (CHead d 
-(Bind Abst) u) n H0 (le_S_n n d0 (le_S (S n) d0 H6))) (S (minus d0 (S n))) 
+n (le_S_n d0 n (le_S_n (S d0) (S n) (le_S (S (S d0)) (S n) (le_n_S (S d0) n 
+H6)))) c0 a0 u0 H4 (CHead d (Bind Abbr) u) H0) a (S O) d0 H5 (eq_ind_r nat 
+(plus (S O) d0) (\lambda (n0: nat).(le n0 n)) H6 (plus d0 (S O)) (plus_sym d0 
+(S O)))) t H1) n (minus_x_SO n (le_lt_trans O d0 n (le_O_n d0) H6)))) (plus 
+(S O) (minus n (S O))) (plus_sym (S O) (minus n (S O)))) (S (plus O (minus n 
+(S O)))) (refl_equal nat (S (plus O (minus n (S O)))))) n (lt_plus_minus O n 
+(le_lt_trans O d0 n (le_O_n d0) H6))))))))))))))))))))) (\lambda (n: 
+nat).(\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (H0: (getl n 
+c0 (CHead d (Bind Abst) u))).(\lambda (t: T).(\lambda (H1: (ty3 g d u 
+t)).(\lambda (H2: ((\forall (e: C).(\forall (u0: T).(\forall (d0: nat).((getl 
+d0 d (CHead e (Bind Abbr) u0)) \to (\forall (a0: C).((csubst1 d0 u0 d a0) \to 
+(\forall (a: C).((drop (S O) d0 a0 a) \to (ex3_2 T T (\lambda (y1: 
+T).(\lambda (_: T).(subst1 d0 u0 u (lift (S O) d0 y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(subst1 d0 u0 t (lift (S O) d0 y2)))) (\lambda (y1: 
+T).(\lambda (y2: T).(ty3 g a y1 y2)))))))))))))).(\lambda (e: C).(\lambda 
+(u0: T).(\lambda (d0: nat).(\lambda (H3: (getl d0 c0 (CHead e (Bind Abbr) 
+u0))).(\lambda (a0: C).(\lambda (H4: (csubst1 d0 u0 c0 a0)).(\lambda (a: 
+C).(\lambda (H5: (drop (S O) d0 a0 a)).(lt_eq_gt_e n d0 (ex3_2 T T (\lambda 
+(y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef n) (lift (S O) d0 y1)))) 
+(\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S n) O u) (lift (S O) 
+d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (H6: 
+(lt n d0)).(let H7 \def (eq_ind nat (minus d0 n) (\lambda (n0: nat).(getl n0 
+(CHead d (Bind Abst) u) (CHead e (Bind Abbr) u0))) (getl_conf_le d0 (CHead e 
+(Bind Abbr) u0) c0 H3 (CHead d (Bind Abst) u) n H0 (le_S_n n d0 (le_S_n (S n) 
+(S d0) (le_S (S (S n)) (S d0) (le_n_S (S n) d0 H6))))) (S (minus d0 (S n))) 
 (minus_x_Sy d0 n H6)) in (ex2_ind C (\lambda (e2: C).(csubst1 (minus d0 n) u0 
 (CHead d (Bind Abst) u) e2)) (\lambda (e2: C).(getl n a0 e2)) (ex3_2 T T 
 (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef n) (lift (S O) d0 
@@ -334,97 +335,97 @@ T).(\lambda (y2: T).(subst1 n0 u0 (lift (S n) O u) (lift (S O) n0 y2))))
 (CHead d (Bind Abst) u) (\lambda (c1: C).(getl n c0 c1)) H0 (CHead e (Bind 
 Abbr) u0) (getl_mono c0 (CHead d (Bind Abst) u) n H0 (CHead e (Bind Abbr) u0) 
 H9)) in (let H11 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: 
-C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow 
-False | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) 
-with [(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with 
-[Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | 
-(Flat _) \Rightarrow False])])) I (CHead e (Bind Abbr) u0) (getl_mono c0 
-(CHead d (Bind Abst) u) n H0 (CHead e (Bind Abbr) u0) H9)) in (False_ind 
-(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 n u0 (TLRef n) (lift (S 
-O) n y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 n u0 (lift (S n) O u) 
-(lift (S O) n y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) 
-H11))) d0 H6))))) (\lambda (H6: (lt d0 n)).(eq_ind_r nat (S (plus O (minus n 
-(S O)))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: 
-T).(subst1 d0 u0 (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda 
-(y2: T).(subst1 d0 u0 (lift (S n) O u) (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind nat (plus (S O) (minus n (S 
-O))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 
-d0 u0 (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
-T).(subst1 d0 u0 (lift (S n) O u) (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind_r nat (plus (minus n (S O)) 
-(S O)) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 
-d0 u0 (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
+C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow 
+(match k with [(Bind b) \Rightarrow (match b with [Abbr \Rightarrow False | 
+Abst \Rightarrow True | Void \Rightarrow False]) | (Flat _) \Rightarrow 
+False])])) I (CHead e (Bind Abbr) u0) (getl_mono c0 (CHead d (Bind Abst) u) n 
+H0 (CHead e (Bind Abbr) u0) H9)) in (False_ind (ex3_2 T T (\lambda (y1: 
+T).(\lambda (_: T).(subst1 n u0 (TLRef n) (lift (S O) n y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(subst1 n u0 (lift (S n) O u) (lift (S O) n y2)))) 
+(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) H11))) d0 H6))))) 
+(\lambda (H6: (lt d0 n)).(eq_ind_r nat (S (plus O (minus n (S O)))) (\lambda 
+(n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef 
+n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 
+(lift (S n) O u) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 
+g a y1 y2))))) (eq_ind nat (plus (S O) (minus n (S O))) (\lambda (n0: 
+nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef n0) 
+(lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S 
+n) O u) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 
+y2))))) (eq_ind_r nat (plus (minus n (S O)) (S O)) (\lambda (n0: nat).(ex3_2 
+T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef n0) (lift (S O) d0 
+y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S n) O u) (lift 
+(S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) 
+(ex3_2_intro T T (\lambda (y1: T).(\lambda (_: T).(subst1 d0 u0 (TLRef (plus 
+(minus n (S O)) (S O))) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
 T).(subst1 d0 u0 (lift (S n) O u) (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))))) (ex3_2_intro T T (\lambda (y1: 
-T).(\lambda (_: T).(subst1 d0 u0 (TLRef (plus (minus n (S O)) (S O))) (lift 
-(S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d0 u0 (lift (S n) O 
-u) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) 
-(TLRef (minus n (S O))) (lift n O u) (eq_ind_r T (TLRef (plus (minus n (S O)) 
-(S O))) (\lambda (t0: T).(subst1 d0 u0 (TLRef (plus (minus n (S O)) (S O))) 
-t0)) (subst1_refl d0 u0 (TLRef (plus (minus n (S O)) (S O)))) (lift (S O) d0 
-(TLRef (minus n (S O)))) (lift_lref_ge (minus n (S O)) (S O) d0 (lt_le_minus 
-d0 n H6))) (eq_ind_r T (lift (plus (S O) n) O u) (\lambda (t0: T).(subst1 d0 
-u0 (lift (S n) O u) t0)) (subst1_refl d0 u0 (lift (S n) O u)) (lift (S O) d0 
-(lift n O u)) (lift_free u n (S O) O d0 (le_S_n d0 (plus O n) (le_S (S d0) 
-(plus O n) H6)) (le_O_n d0))) (eq_ind_r nat (S (minus n (S O))) (\lambda (n0: 
-nat).(ty3 g a (TLRef (minus n (S O))) (lift n0 O u))) (ty3_abst g (minus n (S 
-O)) a d u (getl_drop_conf_ge n (CHead d (Bind Abst) u) a0 (csubst1_getl_ge d0 
-n (le_S_n d0 n (le_S (S d0) n H6)) c0 a0 u0 H4 (CHead d (Bind Abst) u) H0) a 
-(S O) d0 H5 (eq_ind_r nat (plus (S O) d0) (\lambda (n0: nat).(le n0 n)) H6 
-(plus d0 (S O)) (plus_sym d0 (S O)))) t H1) n (minus_x_SO n (le_lt_trans O d0 
-n (le_O_n d0) H6)))) (plus (S O) (minus n (S O))) (plus_sym (S O) (minus n (S 
-O)))) (S (plus O (minus n (S O)))) (refl_equal nat (S (plus O (minus n (S 
-O)))))) n (lt_plus_minus O n (le_lt_trans O d0 n (le_O_n d0) 
-H6))))))))))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (t: 
-T).(\lambda (_: (ty3 g c0 u t)).(\lambda (H1: ((\forall (e: C).(\forall (u0: 
-T).(\forall (d: nat).((getl d c0 (CHead e (Bind Abbr) u0)) \to (\forall (a0: 
-C).((csubst1 d u0 c0 a0) \to (\forall (a: C).((drop (S O) d a0 a) \to (ex3_2 
-T T (\lambda (y1: T).(\lambda (_: T).(subst1 d u0 u (lift (S O) d y1)))) 
-(\lambda (_: T).(\lambda (y2: T).(subst1 d u0 t (lift (S O) d y2)))) (\lambda 
-(y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))))))))))))).(\lambda (b: 
-B).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (ty3 g (CHead c0 (Bind b) 
-u) t3 t4)).(\lambda (H3: ((\forall (e: C).(\forall (u0: T).(\forall (d: 
-nat).((getl d (CHead c0 (Bind b) u) (CHead e (Bind Abbr) u0)) \to (\forall 
-(a0: C).((csubst1 d u0 (CHead c0 (Bind b) u) a0) \to (\forall (a: C).((drop 
-(S O) d a0 a) \to (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d u0 t3 
-(lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d u0 t4 (lift 
-(S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 
-y2)))))))))))))).(\lambda (e: C).(\lambda (u0: T).(\lambda (d: nat).(\lambda 
-(H4: (getl d c0 (CHead e (Bind Abbr) u0))).(\lambda (a0: C).(\lambda (H5: 
-(csubst1 d u0 c0 a0)).(\lambda (a: C).(\lambda (H6: (drop (S O) d a0 a)).(let 
-H7 \def (H1 e u0 d H4 a0 H5 a H6) in (ex3_2_ind T T (\lambda (y1: T).(\lambda 
-(_: T).(subst1 d u0 u (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2: 
+T).(\lambda (y2: T).(ty3 g a y1 y2))) (TLRef (minus n (S O))) (lift n O u) 
+(eq_ind_r T (TLRef (plus (minus n (S O)) (S O))) (\lambda (t0: T).(subst1 d0 
+u0 (TLRef (plus (minus n (S O)) (S O))) t0)) (subst1_refl d0 u0 (TLRef (plus 
+(minus n (S O)) (S O)))) (lift (S O) d0 (TLRef (minus n (S O)))) 
+(lift_lref_ge (minus n (S O)) (S O) d0 (lt_le_minus d0 n H6))) (eq_ind_r T 
+(lift (plus (S O) n) O u) (\lambda (t0: T).(subst1 d0 u0 (lift (S n) O u) 
+t0)) (subst1_refl d0 u0 (lift (S n) O u)) (lift (S O) d0 (lift n O u)) 
+(lift_free u n (S O) O d0 (le_S_n d0 (plus O n) (le_S (S d0) (plus O n) H6)) 
+(le_O_n d0))) (eq_ind_r nat (S (minus n (S O))) (\lambda (n0: nat).(ty3 g a 
+(TLRef (minus n (S O))) (lift n0 O u))) (ty3_abst g (minus n (S O)) a d u 
+(getl_drop_conf_ge n (CHead d (Bind Abst) u) a0 (csubst1_getl_ge d0 n (le_S_n 
+d0 n (le_S_n (S d0) (S n) (le_S (S (S d0)) (S n) (le_n_S (S d0) n H6)))) c0 
+a0 u0 H4 (CHead d (Bind Abst) u) H0) a (S O) d0 H5 (eq_ind_r nat (plus (S O) 
+d0) (\lambda (n0: nat).(le n0 n)) H6 (plus d0 (S O)) (plus_sym d0 (S O)))) t 
+H1) n (minus_x_SO n (le_lt_trans O d0 n (le_O_n d0) H6)))) (plus (S O) (minus 
+n (S O))) (plus_sym (S O) (minus n (S O)))) (S (plus O (minus n (S O)))) 
+(refl_equal nat (S (plus O (minus n (S O)))))) n (lt_plus_minus O n 
+(le_lt_trans O d0 n (le_O_n d0) H6))))))))))))))))))))) (\lambda (c0: 
+C).(\lambda (u: T).(\lambda (t: T).(\lambda (_: (ty3 g c0 u t)).(\lambda (H1: 
+((\forall (e: C).(\forall (u0: T).(\forall (d: nat).((getl d c0 (CHead e 
+(Bind Abbr) u0)) \to (\forall (a0: C).((csubst1 d u0 c0 a0) \to (\forall (a: 
+C).((drop (S O) d a0 a) \to (ex3_2 T T (\lambda (y1: T).(\lambda (_: 
+T).(subst1 d u0 u (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2: 
 T).(subst1 d u0 t (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 
-g a y1 y2))) (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d u0 (THead 
-(Bind b) u t3) (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 
-d u0 (THead (Bind b) u t4) (lift (S O) d y2)))) (\lambda (y1: T).(\lambda 
-(y2: T).(ty3 g a y1 y2)))) (\lambda (x0: T).(\lambda (x1: T).(\lambda (H8: 
-(subst1 d u0 u (lift (S O) d x0))).(\lambda (_: (subst1 d u0 t (lift (S O) d 
-x1))).(\lambda (H10: (ty3 g a x0 x1)).(let H11 \def (H3 e u0 (S d) (getl_head 
-(Bind b) d c0 (CHead e (Bind Abbr) u0) H4 u) (CHead a0 (Bind b) (lift (S O) d 
-x0)) (csubst1_bind b d u0 u (lift (S O) d x0) H8 c0 a0 H5) (CHead a (Bind b) 
-x0) (drop_skip_bind (S O) d a0 a H6 b x0)) in (ex3_2_ind T T (\lambda (y1: 
-T).(\lambda (_: T).(subst1 (S d) u0 t3 (lift (S O) (S d) y1)))) (\lambda (_: 
-T).(\lambda (y2: T).(subst1 (S d) u0 t4 (lift (S O) (S d) y2)))) (\lambda 
-(y1: T).(\lambda (y2: T).(ty3 g (CHead a (Bind b) x0) y1 y2))) (ex3_2 T T 
-(\lambda (y1: T).(\lambda (_: T).(subst1 d u0 (THead (Bind b) u t3) (lift (S 
-O) d y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d u0 (THead (Bind b) u 
-t4) (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) 
-(\lambda (x2: T).(\lambda (x3: T).(\lambda (H12: (subst1 (S d) u0 t3 (lift (S 
-O) (S d) x2))).(\lambda (H13: (subst1 (S d) u0 t4 (lift (S O) (S d) 
-x3))).(\lambda (H14: (ty3 g (CHead a (Bind b) x0) x2 x3)).(ex3_2_intro T T 
-(\lambda (y1: T).(\lambda (_: T).(subst1 d u0 (THead (Bind b) u t3) (lift (S 
-O) d y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d u0 (THead (Bind b) u 
-t4) (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) 
-(THead (Bind b) x0 x2) (THead (Bind b) x0 x3) (eq_ind_r T (THead (Bind b) 
-(lift (S O) d x0) (lift (S O) (S d) x2)) (\lambda (t0: T).(subst1 d u0 (THead 
-(Bind b) u t3) t0)) (subst1_head u0 u (lift (S O) d x0) d H8 (Bind b) t3 
-(lift (S O) (S d) x2) H12) (lift (S O) d (THead (Bind b) x0 x2)) (lift_bind b 
-x0 x2 (S O) d)) (eq_ind_r T (THead (Bind b) (lift (S O) d x0) (lift (S O) (S 
-d) x3)) (\lambda (t0: T).(subst1 d u0 (THead (Bind b) u t4) t0)) (subst1_head 
-u0 u (lift (S O) d x0) d H8 (Bind b) t4 (lift (S O) (S d) x3) H13) (lift (S 
-O) d (THead (Bind b) x0 x3)) (lift_bind b x0 x3 (S O) d)) (ty3_bind g a x0 x1 
-H10 b x2 x3 H14))))))) H11))))))) H7)))))))))))))))))))) (\lambda (c0: 
+g a y1 y2)))))))))))))).(\lambda (b: B).(\lambda (t3: T).(\lambda (t4: 
+T).(\lambda (_: (ty3 g (CHead c0 (Bind b) u) t3 t4)).(\lambda (H3: ((\forall 
+(e: C).(\forall (u0: T).(\forall (d: nat).((getl d (CHead c0 (Bind b) u) 
+(CHead e (Bind Abbr) u0)) \to (\forall (a0: C).((csubst1 d u0 (CHead c0 (Bind 
+b) u) a0) \to (\forall (a: C).((drop (S O) d a0 a) \to (ex3_2 T T (\lambda 
+(y1: T).(\lambda (_: T).(subst1 d u0 t3 (lift (S O) d y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(subst1 d u0 t4 (lift (S O) d y2)))) (\lambda (y1: 
+T).(\lambda (y2: T).(ty3 g a y1 y2)))))))))))))).(\lambda (e: C).(\lambda 
+(u0: T).(\lambda (d: nat).(\lambda (H4: (getl d c0 (CHead e (Bind Abbr) 
+u0))).(\lambda (a0: C).(\lambda (H5: (csubst1 d u0 c0 a0)).(\lambda (a: 
+C).(\lambda (H6: (drop (S O) d a0 a)).(let H7 \def (H1 e u0 d H4 a0 H5 a H6) 
+in (ex3_2_ind T T (\lambda (y1: T).(\lambda (_: T).(subst1 d u0 u (lift (S O) 
+d y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d u0 t (lift (S O) d y2)))) 
+(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) (ex3_2 T T (\lambda (y1: 
+T).(\lambda (_: T).(subst1 d u0 (THead (Bind b) u t3) (lift (S O) d y1)))) 
+(\lambda (_: T).(\lambda (y2: T).(subst1 d u0 (THead (Bind b) u t4) (lift (S 
+O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda 
+(x0: T).(\lambda (x1: T).(\lambda (H8: (subst1 d u0 u (lift (S O) d 
+x0))).(\lambda (_: (subst1 d u0 t (lift (S O) d x1))).(\lambda (H10: (ty3 g a 
+x0 x1)).(let H11 \def (H3 e u0 (S d) (getl_head (Bind b) d c0 (CHead e (Bind 
+Abbr) u0) H4 u) (CHead a0 (Bind b) (lift (S O) d x0)) (csubst1_bind b d u0 u 
+(lift (S O) d x0) H8 c0 a0 H5) (CHead a (Bind b) x0) (drop_skip_bind (S O) d 
+a0 a H6 b x0)) in (ex3_2_ind T T (\lambda (y1: T).(\lambda (_: T).(subst1 (S 
+d) u0 t3 (lift (S O) (S d) y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 (S 
+d) u0 t4 (lift (S O) (S d) y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g 
+(CHead a (Bind b) x0) y1 y2))) (ex3_2 T T (\lambda (y1: T).(\lambda (_: 
+T).(subst1 d u0 (THead (Bind b) u t3) (lift (S O) d y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(subst1 d u0 (THead (Bind b) u t4) (lift (S O) d y2)))) 
+(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (x2: 
+T).(\lambda (x3: T).(\lambda (H12: (subst1 (S d) u0 t3 (lift (S O) (S d) 
+x2))).(\lambda (H13: (subst1 (S d) u0 t4 (lift (S O) (S d) x3))).(\lambda 
+(H14: (ty3 g (CHead a (Bind b) x0) x2 x3)).(ex3_2_intro T T (\lambda (y1: 
+T).(\lambda (_: T).(subst1 d u0 (THead (Bind b) u t3) (lift (S O) d y1)))) 
+(\lambda (_: T).(\lambda (y2: T).(subst1 d u0 (THead (Bind b) u t4) (lift (S 
+O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) (THead (Bind 
+b) x0 x2) (THead (Bind b) x0 x3) (eq_ind_r T (THead (Bind b) (lift (S O) d 
+x0) (lift (S O) (S d) x2)) (\lambda (t0: T).(subst1 d u0 (THead (Bind b) u 
+t3) t0)) (subst1_head u0 u (lift (S O) d x0) d H8 (Bind b) t3 (lift (S O) (S 
+d) x2) H12) (lift (S O) d (THead (Bind b) x0 x2)) (lift_bind b x0 x2 (S O) 
+d)) (eq_ind_r T (THead (Bind b) (lift (S O) d x0) (lift (S O) (S d) x3)) 
+(\lambda (t0: T).(subst1 d u0 (THead (Bind b) u t4) t0)) (subst1_head u0 u 
+(lift (S O) d x0) d H8 (Bind b) t4 (lift (S O) (S d) x3) H13) (lift (S O) d 
+(THead (Bind b) x0 x3)) (lift_bind b x0 x3 (S O) d)) (ty3_bind g a x0 x1 H10 
+b x2 x3 H14))))))) H11))))))) H7)))))))))))))))))))) (\lambda (c0: 
 C).(\lambda (w: T).(\lambda (u: T).(\lambda (_: (ty3 g c0 w u)).(\lambda (H1: 
 ((\forall (e: C).(\forall (u0: T).(\forall (d: nat).((getl d c0 (CHead e 
 (Bind Abbr) u0)) \to (\forall (a0: C).((csubst1 d u0 c0 a0) \to (\forall (a: 
@@ -552,11 +553,8 @@ H12) (lift (S O) d (THead (Flat Cast) x0 x2)) (lift_flat Cast x0 x2 (S O) d))
 O) d x1) d H9 (Flat Cast) t4 (lift (S O) d x0) H8) (lift (S O) d (THead (Flat 
 Cast) x1 x0)) (lift_flat Cast x1 x0 (S O) d)) (ty3_cast g a x2 x0 H15 x1 
 H10)))))))) H11))))))) H7)))))))))))))))))) c t1 t2 H))))).
-(* COMMENTS
-Initial nodes: 12848
-END *)
 
-theorem ty3_gen_cvoid:
+lemma ty3_gen_cvoid:
  \forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c 
 t1 t2) \to (\forall (e: C).(\forall (u: T).(\forall (d: nat).((getl d c 
 (CHead e (Bind Void) u)) \to (\forall (a: C).((drop (S O) d c a) \to (ex3_2 T 
@@ -644,57 +642,58 @@ y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) d0
 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (H5: (lt 
 n d0)).(let H6 \def (eq_ind nat (minus d0 n) (\lambda (n0: nat).(getl n0 
 (CHead d (Bind Abbr) u) (CHead e (Bind Void) u0))) (getl_conf_le d0 (CHead e 
-(Bind Void) u0) c0 H3 (CHead d (Bind Abbr) u) n H0 (le_S_n n d0 (le_S (S n) 
-d0 H5))) (S (minus d0 (S n))) (minus_x_Sy d0 n H5)) in (let H7 \def (eq_ind 
-nat d0 (\lambda (n0: nat).(drop (S O) n0 c0 a)) H4 (S (plus n (minus d0 (S 
-n)))) (lt_plus_minus n d0 H5)) in (ex3_2_ind T C (\lambda (v: T).(\lambda (_: 
-C).(eq T u (lift (S O) (minus d0 (S n)) v)))) (\lambda (v: T).(\lambda (e0: 
-C).(getl n a (CHead e0 (Bind Abbr) v)))) (\lambda (_: T).(\lambda (e0: 
-C).(drop (S O) (minus d0 (S n)) d e0))) (ex3_2 T T (\lambda (y1: T).(\lambda 
+(Bind Void) u0) c0 H3 (CHead d (Bind Abbr) u) n H0 (le_S_n n d0 (le_S_n (S n) 
+(S d0) (le_S (S (S n)) (S d0) (le_n_S (S n) d0 H5))))) (S (minus d0 (S n))) 
+(minus_x_Sy d0 n H5)) in (let H7 \def (eq_ind nat d0 (\lambda (n0: nat).(drop 
+(S O) n0 c0 a)) H4 (S (plus n (minus d0 (S n)))) (lt_plus_minus n d0 H5)) in 
+(ex3_2_ind T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift (S O) (minus d0 
+(S n)) v)))) (\lambda (v: T).(\lambda (e0: C).(getl n a (CHead e0 (Bind Abbr) 
+v)))) (\lambda (_: T).(\lambda (e0: C).(drop (S O) (minus d0 (S n)) d e0))) 
+(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 
+y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) d0 
+y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (x0: 
+T).(\lambda (x1: C).(\lambda (H8: (eq T u (lift (S O) (minus d0 (S n)) 
+x0))).(\lambda (H9: (getl n a (CHead x1 (Bind Abbr) x0))).(\lambda (H10: 
+(drop (S O) (minus d0 (S n)) d x1)).(let H11 \def (eq_ind T u (\lambda (t0: 
+T).(\forall (e0: C).(\forall (u1: T).(\forall (d1: nat).((getl d1 d (CHead e0 
+(Bind Void) u1)) \to (\forall (a0: C).((drop (S O) d1 d a0) \to (ex3_2 T T 
+(\lambda (y1: T).(\lambda (_: T).(eq T t0 (lift (S O) d1 y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(eq T t (lift (S O) d1 y2)))) (\lambda (y1: T).(\lambda 
+(y2: T).(ty3 g a0 y1 y2))))))))))) H2 (lift (S O) (minus d0 (S n)) x0) H8) in 
+(let H12 \def (eq_ind T u (\lambda (t0: T).(ty3 g d t0 t)) H1 (lift (S O) 
+(minus d0 (S n)) x0) H8) in (let H13 \def (H11 e u0 (minus d0 (S n)) 
+(getl_gen_S (Bind Abbr) d (CHead e (Bind Void) u0) u (minus d0 (S n)) H6) x1 
+H10) in (ex3_2_ind T T (\lambda (y1: T).(\lambda (_: T).(eq T (lift (S O) 
+(minus d0 (S n)) x0) (lift (S O) (minus d0 (S n)) y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(eq T t (lift (S O) (minus d0 (S n)) y2)))) (\lambda (y1: 
+T).(\lambda (y2: T).(ty3 g x1 y1 y2))) (ex3_2 T T (\lambda (y1: T).(\lambda 
 (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
 T).(eq T (lift (S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda 
-(y2: T).(ty3 g a y1 y2)))) (\lambda (x0: T).(\lambda (x1: C).(\lambda (H8: 
-(eq T u (lift (S O) (minus d0 (S n)) x0))).(\lambda (H9: (getl n a (CHead x1 
-(Bind Abbr) x0))).(\lambda (H10: (drop (S O) (minus d0 (S n)) d x1)).(let H11 
-\def (eq_ind T u (\lambda (t0: T).(\forall (e0: C).(\forall (u1: T).(\forall 
-(d1: nat).((getl d1 d (CHead e0 (Bind Void) u1)) \to (\forall (a0: C).((drop 
-(S O) d1 d a0) \to (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T t0 (lift 
-(S O) d1 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T t (lift (S O) d1 
-y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a0 y1 y2))))))))))) H2 (lift 
-(S O) (minus d0 (S n)) x0) H8) in (let H12 \def (eq_ind T u (\lambda (t0: 
-T).(ty3 g d t0 t)) H1 (lift (S O) (minus d0 (S n)) x0) H8) in (let H13 \def 
-(H11 e u0 (minus d0 (S n)) (getl_gen_S (Bind Abbr) d (CHead e (Bind Void) u0) 
-u (minus d0 (S n)) H6) x1 H10) in (ex3_2_ind T T (\lambda (y1: T).(\lambda 
-(_: T).(eq T (lift (S O) (minus d0 (S n)) x0) (lift (S O) (minus d0 (S n)) 
-y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T t (lift (S O) (minus d0 (S n)) 
-y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g x1 y1 y2))) (ex3_2 T T 
-(\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) 
-(\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) d0 y2)))) 
-(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (x2: 
-T).(\lambda (x3: T).(\lambda (H14: (eq T (lift (S O) (minus d0 (S n)) x0) 
-(lift (S O) (minus d0 (S n)) x2))).(\lambda (H15: (eq T t (lift (S O) (minus 
-d0 (S n)) x3))).(\lambda (H16: (ty3 g x1 x2 x3)).(let H17 \def (eq_ind T t 
-(\lambda (t0: T).(ty3 g d (lift (S O) (minus d0 (S n)) x0) t0)) H12 (lift (S 
-O) (minus d0 (S n)) x3) H15) in (eq_ind_r T (lift (S O) (minus d0 (S n)) x3) 
-(\lambda (t0: T).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) 
-(lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O 
-t0) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 
-y2))))) (let H18 \def (eq_ind_r T x2 (\lambda (t0: T).(ty3 g x1 t0 x3)) H16 
-x0 (lift_inj x0 x2 (S O) (minus d0 (S n)) H14)) in (eq_ind T (lift (S O) 
-(plus (S n) (minus d0 (S n))) (lift (S n) O x3)) (\lambda (t0: T).(ex3_2 T T 
+(y2: T).(ty3 g a y1 y2)))) (\lambda (x2: T).(\lambda (x3: T).(\lambda (H14: 
+(eq T (lift (S O) (minus d0 (S n)) x0) (lift (S O) (minus d0 (S n)) 
+x2))).(\lambda (H15: (eq T t (lift (S O) (minus d0 (S n)) x3))).(\lambda 
+(H16: (ty3 g x1 x2 x3)).(let H17 \def (eq_ind T t (\lambda (t0: T).(ty3 g d 
+(lift (S O) (minus d0 (S n)) x0) t0)) H12 (lift (S O) (minus d0 (S n)) x3) 
+H15) in (eq_ind_r T (lift (S O) (minus d0 (S n)) x3) (\lambda (t0: T).(ex3_2 
+T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) 
+(\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t0) (lift (S O) d0 
+y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (let H18 \def 
+(eq_ind_r T x2 (\lambda (t0: T).(ty3 g x1 t0 x3)) H16 x0 (lift_inj x0 x2 (S 
+O) (minus d0 (S n)) H14)) in (eq_ind T (lift (S O) (plus (S n) (minus d0 (S 
+n))) (lift (S n) O x3)) (\lambda (t0: T).(ex3_2 T T (\lambda (y1: T).(\lambda 
+(_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
+T).(eq T t0 (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a 
+y1 y2))))) (eq_ind nat d0 (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: 
+T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(eq T (lift (S O) n0 (lift (S n) O x3)) (lift (S O) d0 
+y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (ex3_2_intro T T 
 (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) 
-(\lambda (_: T).(\lambda (y2: T).(eq T t0 (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind nat d0 (\lambda (n0: 
-nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) 
-d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S O) n0 (lift (S n) O 
-x3)) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 
-y2))))) (ex3_2_intro T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) 
-(lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S O) d0 
-(lift (S n) O x3)) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: 
-T).(ty3 g a y1 y2))) (TLRef n) (lift (S n) O x3) (eq_ind_r T (TLRef n) 
-(\lambda (t0: T).(eq T (TLRef n) t0)) (refl_equal T (TLRef n)) (lift (S O) d0 
-(TLRef n)) (lift_lref_lt n (S O) d0 H5)) (refl_equal T (lift (S O) d0 (lift 
-(S n) O x3))) (ty3_abbr g n a x1 x0 H9 x3 H18)) (plus (S n) (minus d0 (S n))) 
+(\lambda (_: T).(\lambda (y2: T).(eq T (lift (S O) d0 (lift (S n) O x3)) 
+(lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) 
+(TLRef n) (lift (S n) O x3) (eq_ind_r T (TLRef n) (\lambda (t0: T).(eq T 
+(TLRef n) t0)) (refl_equal T (TLRef n)) (lift (S O) d0 (TLRef n)) 
+(lift_lref_lt n (S O) d0 H5)) (refl_equal T (lift (S O) d0 (lift (S n) O 
+x3))) (ty3_abbr g n a x1 x0 H9 x3 H18)) (plus (S n) (minus d0 (S n))) 
 (le_plus_minus (S n) d0 H5)) (lift (S n) O (lift (S O) (minus d0 (S n)) x3)) 
 (lift_d x3 (S O) (S n) (minus d0 (S n)) O (le_O_n (minus d0 (S n)))))) t 
 H15))))))) H13))))))))) (getl_drop_conf_lt Abbr c0 d u n H0 a (S O) (minus d0 
@@ -707,128 +706,125 @@ T (lift (S n) O t) (lift (S O) n0 y2)))) (\lambda (y1: T).(\lambda (y2:
 T).(ty3 g a y1 y2))))) (let H8 \def (eq_ind C (CHead d (Bind Abbr) u) 
 (\lambda (c1: C).(getl n c0 c1)) H0 (CHead e (Bind Void) u0) (getl_mono c0 
 (CHead d (Bind Abbr) u) n H0 (CHead e (Bind Void) u0) H7)) in (let H9 \def 
-(eq_ind C (CHead d (Bind Abbr) u) (\lambda (ee: C).(match ee in C return 
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) 
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b) 
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow 
-True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat _) 
-\Rightarrow False])])) I (CHead e (Bind Void) u0) (getl_mono c0 (CHead d 
-(Bind Abbr) u) n H0 (CHead e (Bind Void) u0) H7)) in (False_ind (ex3_2 T T 
-(\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) n y1)))) 
-(\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) n y2)))) 
-(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) H9))) d0 H5)))) (\lambda 
-(H5: (lt d0 n)).(eq_ind_r nat (S (plus O (minus n (S O)))) (\lambda (n0: 
-nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n0) (lift (S O) 
-d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) 
-d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind nat 
-(plus (S O) (minus n (S O))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: 
+(eq_ind C (CHead d (Bind Abbr) u) (\lambda (ee: C).(match ee with [(CSort _) 
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind b) 
+\Rightarrow (match b with [Abbr \Rightarrow True | Abst \Rightarrow False | 
+Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead e (Bind 
+Void) u0) (getl_mono c0 (CHead d (Bind Abbr) u) n H0 (CHead e (Bind Void) u0) 
+H7)) in (False_ind (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef 
+n) (lift (S O) n y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O 
+t) (lift (S O) n y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) 
+H9))) d0 H5)))) (\lambda (H5: (lt d0 n)).(eq_ind_r nat (S (plus O (minus n (S 
+O)))) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T 
+(TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift 
+(S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a 
+y1 y2))))) (eq_ind nat (plus (S O) (minus n (S O))) (\lambda (n0: nat).(ex3_2 
+T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n0) (lift (S O) d0 y1)))) 
+(\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) d0 y2)))) 
+(\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind_r nat (plus 
+(minus n (S O)) (S O)) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: 
 T).(\lambda (_: T).(eq T (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: 
 T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) d0 y2)))) (\lambda 
-(y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (eq_ind_r nat (plus (minus n (S 
-O)) (S O)) (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq 
-T (TLRef n0) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T 
-(lift (S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 
-g a y1 y2))))) (ex3_2_intro T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef 
-(plus (minus n (S O)) (S O))) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda 
-(y2: T).(eq T (lift (S n) O t) (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))) (TLRef (minus n (S O))) (lift n O t) 
-(eq_ind_r T (TLRef (plus (minus n (S O)) (S O))) (\lambda (t0: T).(eq T 
-(TLRef (plus (minus n (S O)) (S O))) t0)) (refl_equal T (TLRef (plus (minus n 
-(S O)) (S O)))) (lift (S O) d0 (TLRef (minus n (S O)))) (lift_lref_ge (minus 
-n (S O)) (S O) d0 (lt_le_minus d0 n H5))) (eq_ind_r T (lift (plus (S O) n) O 
-t) (\lambda (t0: T).(eq T (lift (S n) O t) t0)) (refl_equal T (lift (S n) O 
-t)) (lift (S O) d0 (lift n O t)) (lift_free t n (S O) O d0 (le_S_n d0 (plus O 
-n) (le_S (S d0) (plus O n) H5)) (le_O_n d0))) (eq_ind_r nat (S (minus n (S 
-O))) (\lambda (n0: nat).(ty3 g a (TLRef (minus n (S O))) (lift n0 O t))) 
-(ty3_abbr g (minus n (S O)) a d u (getl_drop_conf_ge n (CHead d (Bind Abbr) 
-u) c0 H0 a (S O) d0 H4 (eq_ind_r nat (plus (S O) d0) (\lambda (n0: nat).(le 
-n0 n)) H5 (plus d0 (S O)) (plus_sym d0 (S O)))) t H1) n (minus_x_SO n 
-(le_lt_trans O d0 n (le_O_n d0) H5)))) (plus (S O) (minus n (S O))) (plus_sym 
-(S O) (minus n (S O)))) (S (plus O (minus n (S O)))) (refl_equal nat (S (plus 
-O (minus n (S O)))))) n (lt_plus_minus O n (le_lt_trans O d0 n (le_O_n d0) 
-H5))))))))))))))))))) (\lambda (n: nat).(\lambda (c0: C).(\lambda (d: 
-C).(\lambda (u: T).(\lambda (H0: (getl n c0 (CHead d (Bind Abst) 
-u))).(\lambda (t: T).(\lambda (H1: (ty3 g d u t)).(\lambda (H2: ((\forall (e: 
-C).(\forall (u0: T).(\forall (d0: nat).((getl d0 d (CHead e (Bind Void) u0)) 
-\to (\forall (a: C).((drop (S O) d0 d a) \to (ex3_2 T T (\lambda (y1: 
-T).(\lambda (_: T).(eq T u (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda 
-(y2: T).(eq T t (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 
-g a y1 y2)))))))))))).(\lambda (e: C).(\lambda (u0: T).(\lambda (d0: 
-nat).(\lambda (H3: (getl d0 c0 (CHead e (Bind Void) u0))).(\lambda (a: 
-C).(\lambda (H4: (drop (S O) d0 c0 a)).(lt_eq_gt_e n d0 (ex3_2 T T (\lambda 
-(y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: 
-T).(\lambda (y2: T).(eq T (lift (S n) O u) (lift (S O) d0 y2)))) (\lambda 
-(y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (H5: (lt n d0)).(let H6 
-\def (eq_ind nat (minus d0 n) (\lambda (n0: nat).(getl n0 (CHead d (Bind 
-Abst) u) (CHead e (Bind Void) u0))) (getl_conf_le d0 (CHead e (Bind Void) u0) 
-c0 H3 (CHead d (Bind Abst) u) n H0 (le_S_n n d0 (le_S (S n) d0 H5))) (S 
-(minus d0 (S n))) (minus_x_Sy d0 n H5)) in (let H7 \def (eq_ind nat d0 
-(\lambda (n0: nat).(drop (S O) n0 c0 a)) H4 (S (plus n (minus d0 (S n)))) 
-(lt_plus_minus n d0 H5)) in (ex3_2_ind T C (\lambda (v: T).(\lambda (_: 
-C).(eq T u (lift (S O) (minus d0 (S n)) v)))) (\lambda (v: T).(\lambda (e0: 
-C).(getl n a (CHead e0 (Bind Abst) v)))) (\lambda (_: T).(\lambda (e0: 
-C).(drop (S O) (minus d0 (S n)) d e0))) (ex3_2 T T (\lambda (y1: T).(\lambda 
+(y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (ex3_2_intro T T (\lambda (y1: 
+T).(\lambda (_: T).(eq T (TLRef (plus (minus n (S O)) (S O))) (lift (S O) d0 
+y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O t) (lift (S O) d0 
+y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) (TLRef (minus n (S 
+O))) (lift n O t) (eq_ind_r T (TLRef (plus (minus n (S O)) (S O))) (\lambda 
+(t0: T).(eq T (TLRef (plus (minus n (S O)) (S O))) t0)) (refl_equal T (TLRef 
+(plus (minus n (S O)) (S O)))) (lift (S O) d0 (TLRef (minus n (S O)))) 
+(lift_lref_ge (minus n (S O)) (S O) d0 (lt_le_minus d0 n H5))) (eq_ind_r T 
+(lift (plus (S O) n) O t) (\lambda (t0: T).(eq T (lift (S n) O t) t0)) 
+(refl_equal T (lift (S n) O t)) (lift (S O) d0 (lift n O t)) (lift_free t n 
+(S O) O d0 (le_S_n d0 (plus O n) (le_S (S d0) (plus O n) H5)) (le_O_n d0))) 
+(eq_ind_r nat (S (minus n (S O))) (\lambda (n0: nat).(ty3 g a (TLRef (minus n 
+(S O))) (lift n0 O t))) (ty3_abbr g (minus n (S O)) a d u (getl_drop_conf_ge 
+n (CHead d (Bind Abbr) u) c0 H0 a (S O) d0 H4 (eq_ind_r nat (plus (S O) d0) 
+(\lambda (n0: nat).(le n0 n)) H5 (plus d0 (S O)) (plus_sym d0 (S O)))) t H1) 
+n (minus_x_SO n (le_lt_trans O d0 n (le_O_n d0) H5)))) (plus (S O) (minus n 
+(S O))) (plus_sym (S O) (minus n (S O)))) (S (plus O (minus n (S O)))) 
+(refl_equal nat (S (plus O (minus n (S O)))))) n (lt_plus_minus O n 
+(le_lt_trans O d0 n (le_O_n d0) H5))))))))))))))))))) (\lambda (n: 
+nat).(\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (H0: (getl n 
+c0 (CHead d (Bind Abst) u))).(\lambda (t: T).(\lambda (H1: (ty3 g d u 
+t)).(\lambda (H2: ((\forall (e: C).(\forall (u0: T).(\forall (d0: nat).((getl 
+d0 d (CHead e (Bind Void) u0)) \to (\forall (a: C).((drop (S O) d0 d a) \to 
+(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T u (lift (S O) d0 y1)))) 
+(\lambda (_: T).(\lambda (y2: T).(eq T t (lift (S O) d0 y2)))) (\lambda (y1: 
+T).(\lambda (y2: T).(ty3 g a y1 y2)))))))))))).(\lambda (e: C).(\lambda (u0: 
+T).(\lambda (d0: nat).(\lambda (H3: (getl d0 c0 (CHead e (Bind Void) 
+u0))).(\lambda (a: C).(\lambda (H4: (drop (S O) d0 c0 a)).(lt_eq_gt_e n d0 
+(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 
+y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O u) (lift (S O) d0 
+y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (H5: (lt 
+n d0)).(let H6 \def (eq_ind nat (minus d0 n) (\lambda (n0: nat).(getl n0 
+(CHead d (Bind Abst) u) (CHead e (Bind Void) u0))) (getl_conf_le d0 (CHead e 
+(Bind Void) u0) c0 H3 (CHead d (Bind Abst) u) n H0 (le_S_n n d0 (le_S_n (S n) 
+(S d0) (le_S (S (S n)) (S d0) (le_n_S (S n) d0 H5))))) (S (minus d0 (S n))) 
+(minus_x_Sy d0 n H5)) in (let H7 \def (eq_ind nat d0 (\lambda (n0: nat).(drop 
+(S O) n0 c0 a)) H4 (S (plus n (minus d0 (S n)))) (lt_plus_minus n d0 H5)) in 
+(ex3_2_ind T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift (S O) (minus d0 
+(S n)) v)))) (\lambda (v: T).(\lambda (e0: C).(getl n a (CHead e0 (Bind Abst) 
+v)))) (\lambda (_: T).(\lambda (e0: C).(drop (S O) (minus d0 (S n)) d e0))) 
+(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 
+y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O u) (lift (S O) d0 
+y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) (\lambda (x0: 
+T).(\lambda (x1: C).(\lambda (H8: (eq T u (lift (S O) (minus d0 (S n)) 
+x0))).(\lambda (H9: (getl n a (CHead x1 (Bind Abst) x0))).(\lambda (H10: 
+(drop (S O) (minus d0 (S n)) d x1)).(let H11 \def (eq_ind T u (\lambda (t0: 
+T).(\forall (e0: C).(\forall (u1: T).(\forall (d1: nat).((getl d1 d (CHead e0 
+(Bind Void) u1)) \to (\forall (a0: C).((drop (S O) d1 d a0) \to (ex3_2 T T 
+(\lambda (y1: T).(\lambda (_: T).(eq T t0 (lift (S O) d1 y1)))) (\lambda (_: 
+T).(\lambda (y2: T).(eq T t (lift (S O) d1 y2)))) (\lambda (y1: T).(\lambda 
+(y2: T).(ty3 g a0 y1 y2))))))))))) H2 (lift (S O) (minus d0 (S n)) x0) H8) in 
+(let H12 \def (eq_ind T u (\lambda (t0: T).(ty3 g d t0 t)) H1 (lift (S O) 
+(minus d0 (S n)) x0) H8) in (eq_ind_r T (lift (S O) (minus d0 (S n)) x0) 
+(\lambda (t0: T).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) 
+(lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O 
+t0) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 
+y2))))) (let H13 \def (H11 e u0 (minus d0 (S n)) (getl_gen_S (Bind Abst) d 
+(CHead e (Bind Void) u0) u (minus d0 (S n)) H6) x1 H10) in (ex3_2_ind T T 
+(\lambda (y1: T).(\lambda (_: T).(eq T (lift (S O) (minus d0 (S n)) x0) (lift 
+(S O) (minus d0 (S n)) y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T t (lift 
+(S O) (minus d0 (S n)) y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g x1 y1 
+y2))) (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) 
+d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O (lift (S O) 
+(minus d0 (S n)) x0)) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: 
+T).(ty3 g a y1 y2)))) (\lambda (x2: T).(\lambda (x3: T).(\lambda (H14: (eq T 
+(lift (S O) (minus d0 (S n)) x0) (lift (S O) (minus d0 (S n)) x2))).(\lambda 
+(H15: (eq T t (lift (S O) (minus d0 (S n)) x3))).(\lambda (H16: (ty3 g x1 x2 
+x3)).(let H17 \def (eq_ind T t (\lambda (t0: T).(ty3 g d (lift (S O) (minus 
+d0 (S n)) x0) t0)) H12 (lift (S O) (minus d0 (S n)) x3) H15) in (let H18 \def 
+(eq_ind_r T x2 (\lambda (t0: T).(ty3 g x1 t0 x3)) H16 x0 (lift_inj x0 x2 (S 
+O) (minus d0 (S n)) H14)) in (eq_ind T (lift (S O) (plus (S n) (minus d0 (S 
+n))) (lift (S n) O x0)) (\lambda (t0: T).(ex3_2 T T (\lambda (y1: T).(\lambda 
 (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: 
-T).(eq T (lift (S n) O u) (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda 
-(y2: T).(ty3 g a y1 y2)))) (\lambda (x0: T).(\lambda (x1: C).(\lambda (H8: 
-(eq T u (lift (S O) (minus d0 (S n)) x0))).(\lambda (H9: (getl n a (CHead x1 
-(Bind Abst) x0))).(\lambda (H10: (drop (S O) (minus d0 (S n)) d x1)).(let H11 
-\def (eq_ind T u (\lambda (t0: T).(\forall (e0: C).(\forall (u1: T).(\forall 
-(d1: nat).((getl d1 d (CHead e0 (Bind Void) u1)) \to (\forall (a0: C).((drop 
-(S O) d1 d a0) \to (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T t0 (lift 
-(S O) d1 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T t (lift (S O) d1 
-y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a0 y1 y2))))))))))) H2 (lift 
-(S O) (minus d0 (S n)) x0) H8) in (let H12 \def (eq_ind T u (\lambda (t0: 
-T).(ty3 g d t0 t)) H1 (lift (S O) (minus d0 (S n)) x0) H8) in (eq_ind_r T 
-(lift (S O) (minus d0 (S n)) x0) (\lambda (t0: T).(ex3_2 T T (\lambda (y1: 
-T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: 
-T).(\lambda (y2: T).(eq T (lift (S n) O t0) (lift (S O) d0 y2)))) (\lambda 
-(y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (let H13 \def (H11 e u0 (minus 
-d0 (S n)) (getl_gen_S (Bind Abst) d (CHead e (Bind Void) u0) u (minus d0 (S 
-n)) H6) x1 H10) in (ex3_2_ind T T (\lambda (y1: T).(\lambda (_: T).(eq T 
-(lift (S O) (minus d0 (S n)) x0) (lift (S O) (minus d0 (S n)) y1)))) (\lambda 
-(_: T).(\lambda (y2: T).(eq T t (lift (S O) (minus d0 (S n)) y2)))) (\lambda 
-(y1: T).(\lambda (y2: T).(ty3 g x1 y1 y2))) (ex3_2 T T (\lambda (y1: 
-T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: 
-T).(\lambda (y2: T).(eq T (lift (S n) O (lift (S O) (minus d0 (S n)) x0)) 
-(lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2)))) 
-(\lambda (x2: T).(\lambda (x3: T).(\lambda (H14: (eq T (lift (S O) (minus d0 
-(S n)) x0) (lift (S O) (minus d0 (S n)) x2))).(\lambda (H15: (eq T t (lift (S 
-O) (minus d0 (S n)) x3))).(\lambda (H16: (ty3 g x1 x2 x3)).(let H17 \def 
-(eq_ind T t (\lambda (t0: T).(ty3 g d (lift (S O) (minus d0 (S n)) x0) t0)) 
-H12 (lift (S O) (minus d0 (S n)) x3) H15) in (let H18 \def (eq_ind_r T x2 
-(\lambda (t0: T).(ty3 g x1 t0 x3)) H16 x0 (lift_inj x0 x2 (S O) (minus d0 (S 
-n)) H14)) in (eq_ind T (lift (S O) (plus (S n) (minus d0 (S n))) (lift (S n) 
-O x0)) (\lambda (t0: T).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T 
-(TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T t0 
-(lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) 
-(eq_ind nat d0 (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: 
-T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq 
-T (lift (S O) n0 (lift (S n) O x0)) (lift (S O) d0 y2)))) (\lambda (y1: 
-T).(\lambda (y2: T).(ty3 g a y1 y2))))) (ex3_2_intro T T (\lambda (y1: 
+T).(eq T t0 (lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a 
+y1 y2))))) (eq_ind nat d0 (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: 
 T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) (\lambda (_: 
-T).(\lambda (y2: T).(eq T (lift (S O) d0 (lift (S n) O x0)) (lift (S O) d0 
-y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) (TLRef n) (lift (S 
-n) O x0) (eq_ind_r T (TLRef n) (\lambda (t0: T).(eq T (TLRef n) t0)) 
-(refl_equal T (TLRef n)) (lift (S O) d0 (TLRef n)) (lift_lref_lt n (S O) d0 
-H5)) (refl_equal T (lift (S O) d0 (lift (S n) O x0))) (ty3_abst g n a x1 x0 
-H9 x3 H18)) (plus (S n) (minus d0 (S n))) (le_plus_minus (S n) d0 H5)) (lift 
-(S n) O (lift (S O) (minus d0 (S n)) x0)) (lift_d x0 (S O) (S n) (minus d0 (S 
-n)) O (le_O_n (minus d0 (S n)))))))))))) H13)) u H8)))))))) 
-(getl_drop_conf_lt Abst c0 d u n H0 a (S O) (minus d0 (S n)) H7))))) (\lambda 
-(H5: (eq nat n d0)).(let H6 \def (eq_ind_r nat d0 (\lambda (n0: nat).(drop (S 
-O) n0 c0 a)) H4 n H5) in (let H7 \def (eq_ind_r nat d0 (\lambda (n0: 
-nat).(getl n0 c0 (CHead e (Bind Void) u0))) H3 n H5) in (eq_ind nat n 
-(\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef 
-n) (lift (S O) n0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq T (lift (S n) O 
-u) (lift (S O) n0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 
-y2))))) (let H8 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (c1: C).(getl 
-n c0 c1)) H0 (CHead e (Bind Void) u0) (getl_mono c0 (CHead d (Bind Abst) u) n 
-H0 (CHead e (Bind Void) u0) H7)) in (let H9 \def (eq_ind C (CHead d (Bind 
-Abst) u) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with 
-[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return 
-(\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B return 
-(\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow True | 
+T).(\lambda (y2: T).(eq T (lift (S O) n0 (lift (S n) O x0)) (lift (S O) d0 
+y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))) (ex3_2_intro T T 
+(\lambda (y1: T).(\lambda (_: T).(eq T (TLRef n) (lift (S O) d0 y1)))) 
+(\lambda (_: T).(\lambda (y2: T).(eq T (lift (S O) d0 (lift (S n) O x0)) 
+(lift (S O) d0 y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) 
+(TLRef n) (lift (S n) O x0) (eq_ind_r T (TLRef n) (\lambda (t0: T).(eq T 
+(TLRef n) t0)) (refl_equal T (TLRef n)) (lift (S O) d0 (TLRef n)) 
+(lift_lref_lt n (S O) d0 H5)) (refl_equal T (lift (S O) d0 (lift (S n) O 
+x0))) (ty3_abst g n a x1 x0 H9 x3 H18)) (plus (S n) (minus d0 (S n))) 
+(le_plus_minus (S n) d0 H5)) (lift (S n) O (lift (S O) (minus d0 (S n)) x0)) 
+(lift_d x0 (S O) (S n) (minus d0 (S n)) O (le_O_n (minus d0 (S n)))))))))))) 
+H13)) u H8)))))))) (getl_drop_conf_lt Abst c0 d u n H0 a (S O) (minus d0 (S 
+n)) H7))))) (\lambda (H5: (eq nat n d0)).(let H6 \def (eq_ind_r nat d0 
+(\lambda (n0: nat).(drop (S O) n0 c0 a)) H4 n H5) in (let H7 \def (eq_ind_r 
+nat d0 (\lambda (n0: nat).(getl n0 c0 (CHead e (Bind Void) u0))) H3 n H5) in 
+(eq_ind nat n (\lambda (n0: nat).(ex3_2 T T (\lambda (y1: T).(\lambda (_: 
+T).(eq T (TLRef n) (lift (S O) n0 y1)))) (\lambda (_: T).(\lambda (y2: T).(eq 
+T (lift (S n) O u) (lift (S O) n0 y2)))) (\lambda (y1: T).(\lambda (y2: 
+T).(ty3 g a y1 y2))))) (let H8 \def (eq_ind C (CHead d (Bind Abst) u) 
+(\lambda (c1: C).(getl n c0 c1)) H0 (CHead e (Bind Void) u0) (getl_mono c0 
+(CHead d (Bind Abst) u) n H0 (CHead e (Bind Void) u0) H7)) in (let H9 \def 
+(eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: C).(match ee with [(CSort _) 
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind b) 
+\Rightarrow (match b with [Abbr \Rightarrow False | Abst \Rightarrow True | 
 Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead e (Bind 
 Void) u0) (getl_mono c0 (CHead d (Bind Abst) u) n H0 (CHead e (Bind Void) u0) 
 H7)) in (False_ind (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(eq T (TLRef 
@@ -1096,7 +1092,4 @@ x2 x0 H19 x1 H9)) (THead (Flat Cast) (lift (S O) d x1) (lift (S O) d x0))
 (lift_flat Cast x1 x0 (S O) d)) (THead (Flat Cast) (lift (S O) d x0) (lift (S 
 O) d x2)) (lift_flat Cast x0 x2 (S O) d))) t3 H15))))))) H14)) t4 H7)))) t0 
 H8))))))) H6)))))))))))))))) c t1 t2 H))))).
-(* COMMENTS
-Initial nodes: 13105
-END *)