(* 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
(\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
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:
(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
(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:
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
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
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
(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 *)
projects / helm.git / blobdiff