(* This file was automatically generated: do not edit *********************)
-set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/subst1".
+include "LambdaDelta-1/ty3/props.ma".
-include "ty3/props.ma".
+include "LambdaDelta-1/pc3/subst1.ma".
-include "pc3/subst1.ma".
-
-include "pc3/fwd.ma".
-
-include "csubst1/getl.ma".
-
-include "csubst1/fwd.ma".
-
-include "getl/getl.ma".
+include "LambdaDelta-1/getl/getl.ma".
theorem ty3_gen_cabbr:
\forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c
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_comm 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_comm (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)
+(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:
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_comm 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_comm (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)
+(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:
(Bind Abst) u t)) (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 d u0 w
(lift (S O) d x2))).(\lambda (H13: (subst1 d u0 u (lift (S O) d
-x3))).(\lambda (H14: (ty3 g a x2 x3)).(ex3_2_ind T T (\lambda (u2:
-T).(\lambda (t3: T).(eq T (lift (S O) d x1) (THead (Bind Abst) u2 t3))))
-(\lambda (u2: T).(\lambda (_: T).(subst1 d u0 u u2))) (\lambda (_:
-T).(\lambda (t3: T).(subst1 (s (Bind Abst) d) u0 t t3))) (ex3_2 T T (\lambda
-(y1: T).(\lambda (_: T).(subst1 d u0 (THead (Flat Appl) w v) (lift (S O) d
-y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d u0 (THead (Flat Appl) w
-(THead (Bind Abst) u t)) (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2:
-T).(ty3 g a y1 y2)))) (\lambda (x4: T).(\lambda (x5: T).(\lambda (H15: (eq T
-(lift (S O) d x1) (THead (Bind Abst) x4 x5))).(\lambda (H16: (subst1 d u0 u
-x4)).(\lambda (H17: (subst1 (s (Bind Abst) d) u0 t x5)).(let H18 \def (sym_eq
-T (lift (S O) d x1) (THead (Bind Abst) x4 x5) H15) in (ex3_2_ind T T (\lambda
-(y: T).(\lambda (z: T).(eq T x1 (THead (Bind Abst) y z)))) (\lambda (y:
+x3))).(\lambda (H14: (ty3 g a x2 x3)).(let H_x \def (subst1_gen_head (Bind
+Abst) u0 u t (lift (S O) d x1) d H9) in (let H15 \def H_x in (ex3_2_ind T T
+(\lambda (u2: T).(\lambda (t3: T).(eq T (lift (S O) d x1) (THead (Bind Abst)
+u2 t3)))) (\lambda (u2: T).(\lambda (_: T).(subst1 d u0 u u2))) (\lambda (_:
+T).(\lambda (t3: T).(subst1 (S d) u0 t t3))) (ex3_2 T T (\lambda (y1:
+T).(\lambda (_: T).(subst1 d u0 (THead (Flat Appl) w v) (lift (S O) d y1))))
+(\lambda (_: T).(\lambda (y2: T).(subst1 d u0 (THead (Flat Appl) w (THead
+(Bind Abst) u t)) (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3
+g a y1 y2)))) (\lambda (x4: T).(\lambda (x5: T).(\lambda (H16: (eq T (lift (S
+O) d x1) (THead (Bind Abst) x4 x5))).(\lambda (H17: (subst1 d u0 u
+x4)).(\lambda (H18: (subst1 (S d) u0 t x5)).(let H19 \def (sym_eq T (lift (S
+O) d x1) (THead (Bind Abst) x4 x5) H16) in (ex3_2_ind T T (\lambda (y:
+T).(\lambda (z: T).(eq T x1 (THead (Bind Abst) y z)))) (\lambda (y:
T).(\lambda (_: T).(eq T x4 (lift (S O) d y)))) (\lambda (_: T).(\lambda (z:
T).(eq T x5 (lift (S O) (S d) z)))) (ex3_2 T T (\lambda (y1: T).(\lambda (_:
T).(subst1 d u0 (THead (Flat Appl) w v) (lift (S O) d y1)))) (\lambda (_:
T).(\lambda (y2: T).(subst1 d u0 (THead (Flat Appl) w (THead (Bind Abst) u
t)) (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))))
-(\lambda (x6: T).(\lambda (x7: T).(\lambda (H19: (eq T x1 (THead (Bind Abst)
-x6 x7))).(\lambda (H20: (eq T x4 (lift (S O) d x6))).(\lambda (H21: (eq T x5
-(lift (S O) (S d) x7))).(let H22 \def (eq_ind T x5 (\lambda (t0: T).(subst1
-(s (Bind Abst) d) u0 t t0)) H17 (lift (S O) (S d) x7) H21) in (let H23 \def
-(eq_ind T x4 (\lambda (t0: T).(subst1 d u0 u t0)) H16 (lift (S O) d x6) H20)
-in (let H24 \def (eq_ind T x1 (\lambda (t0: T).(ty3 g a x0 t0)) H10 (THead
-(Bind Abst) x6 x7) H19) in (let H25 \def (eq_ind T x6 (\lambda (t0: T).(ty3 g
-a x0 (THead (Bind Abst) t0 x7))) H24 x3 (subst1_confluence_lift u x6 u0 d H23
-x3 H13)) in (ex3_2_intro T T (\lambda (y1: T).(\lambda (_: T).(subst1 d u0
-(THead (Flat Appl) w v) (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2:
-T).(subst1 d u0 (THead (Flat Appl) w (THead (Bind Abst) u t)) (lift (S O) d
-y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) (THead (Flat Appl)
-x2 x0) (THead (Flat Appl) x2 (THead (Bind Abst) x3 x7)) (eq_ind_r T (THead
-(Flat Appl) (lift (S O) d x2) (lift (S O) d x0)) (\lambda (t0: T).(subst1 d
-u0 (THead (Flat Appl) w v) t0)) (subst1_head u0 w (lift (S O) d x2) d H12
-(Flat Appl) v (lift (S O) d x0) H8) (lift (S O) d (THead (Flat Appl) x2 x0))
-(lift_flat Appl x2 x0 (S O) d)) (eq_ind_r T (THead (Flat Appl) (lift (S O) d
-x2) (lift (S O) d (THead (Bind Abst) x3 x7))) (\lambda (t0: T).(subst1 d u0
-(THead (Flat Appl) w (THead (Bind Abst) u t)) t0)) (subst1_head u0 w (lift (S
-O) d x2) d H12 (Flat Appl) (THead (Bind Abst) u t) (lift (S O) d (THead (Bind
+(\lambda (x6: T).(\lambda (x7: T).(\lambda (H20: (eq T x1 (THead (Bind Abst)
+x6 x7))).(\lambda (H21: (eq T x4 (lift (S O) d x6))).(\lambda (H22: (eq T x5
+(lift (S O) (S d) x7))).(let H23 \def (eq_ind T x5 (\lambda (t0: T).(subst1
+(S d) u0 t t0)) H18 (lift (S O) (S d) x7) H22) in (let H24 \def (eq_ind T x4
+(\lambda (t0: T).(subst1 d u0 u t0)) H17 (lift (S O) d x6) H21) in (let H25
+\def (eq_ind T x1 (\lambda (t0: T).(ty3 g a x0 t0)) H10 (THead (Bind Abst) x6
+x7) H20) in (let H26 \def (eq_ind T x6 (\lambda (t0: T).(ty3 g a x0 (THead
+(Bind Abst) t0 x7))) H25 x3 (subst1_confluence_lift u x6 u0 d H24 x3 H13)) in
+(ex3_2_intro T T (\lambda (y1: T).(\lambda (_: T).(subst1 d u0 (THead (Flat
+Appl) w v) (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d u0
+(THead (Flat Appl) w (THead (Bind Abst) u t)) (lift (S O) d y2)))) (\lambda
+(y1: T).(\lambda (y2: T).(ty3 g a y1 y2))) (THead (Flat Appl) x2 x0) (THead
+(Flat Appl) x2 (THead (Bind Abst) x3 x7)) (eq_ind_r T (THead (Flat Appl)
+(lift (S O) d x2) (lift (S O) d x0)) (\lambda (t0: T).(subst1 d u0 (THead
+(Flat Appl) w v) t0)) (subst1_head u0 w (lift (S O) d x2) d H12 (Flat Appl) v
+(lift (S O) d x0) H8) (lift (S O) d (THead (Flat Appl) x2 x0)) (lift_flat
+Appl x2 x0 (S O) d)) (eq_ind_r T (THead (Flat Appl) (lift (S O) d x2) (lift
+(S O) d (THead (Bind Abst) x3 x7))) (\lambda (t0: T).(subst1 d u0 (THead
+(Flat Appl) w (THead (Bind Abst) u t)) t0)) (subst1_head u0 w (lift (S O) d
+x2) d H12 (Flat Appl) (THead (Bind Abst) u t) (lift (S O) d (THead (Bind
Abst) x3 x7)) (eq_ind_r T (THead (Bind Abst) (lift (S O) d x3) (lift (S O) (S
d) x7)) (\lambda (t0: T).(subst1 (s (Flat Appl) d) u0 (THead (Bind Abst) u t)
t0)) (subst1_head u0 u (lift (S O) d x3) (s (Flat Appl) d) H13 (Bind Abst) t
-(lift (S O) (S d) x7) H22) (lift (S O) d (THead (Bind Abst) x3 x7))
+(lift (S O) (S d) x7) H23) (lift (S O) d (THead (Bind Abst) x3 x7))
(lift_bind Abst x3 x7 (S O) d))) (lift (S O) d (THead (Flat Appl) x2 (THead
(Bind Abst) x3 x7))) (lift_flat Appl x2 (THead (Bind Abst) x3 x7) (S O) d))
-(ty3_appl g a x2 x3 H14 x0 x7 H25))))))))))) (lift_gen_bind Abst x4 x5 x1 (S
-O) d H18)))))))) (subst1_gen_head (Bind Abst) u0 u t (lift (S O) d x1) d
-H9))))))) H11))))))) H7))))))))))))))))))) (\lambda (c0: C).(\lambda (t3:
-T).(\lambda (t4: T).(\lambda (_: (ty3 g c0 t3 t4)).(\lambda (H1: ((\forall
-(e: C).(\forall (u: T).(\forall (d: nat).((getl d c0 (CHead e (Bind Abbr) u))
-\to (\forall (a0: C).((csubst1 d u c0 a0) \to (\forall (a: C).((drop (S O) d
-a0 a) \to (ex3_2 T T (\lambda (y1: T).(\lambda (_: T).(subst1 d u t3 (lift (S
-O) d y1)))) (\lambda (_: T).(\lambda (y2: T).(subst1 d u t4 (lift (S O) d
-y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3 g a y1
-y2)))))))))))))).(\lambda (t0: T).(\lambda (_: (ty3 g c0 t4 t0)).(\lambda
-(H3: ((\forall (e: C).(\forall (u: T).(\forall (d: nat).((getl d c0 (CHead e
+(ty3_appl g a x2 x3 H14 x0 x7 H26))))))))))) (lift_gen_bind Abst x4 x5 x1 (S
+O) d H19)))))))) H15)))))))) H11))))))) H7))))))))))))))))))) (\lambda (c0:
+C).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (ty3 g c0 t3 t4)).(\lambda
+(H1: ((\forall (e: C).(\forall (u: T).(\forall (d: nat).((getl d c0 (CHead e
(Bind Abbr) u)) \to (\forall (a0: C).((csubst1 d u c0 a0) \to (\forall (a:
C).((drop (S O) d a0 a) \to (ex3_2 T T (\lambda (y1: T).(\lambda (_:
-T).(subst1 d u t4 (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2:
+T).(subst1 d u t3 (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2:
+T).(subst1 d u t4 (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3
+g a y1 y2)))))))))))))).(\lambda (t0: T).(\lambda (_: (ty3 g c0 t4
+t0)).(\lambda (H3: ((\forall (e: C).(\forall (u: T).(\forall (d: nat).((getl
+d c0 (CHead e (Bind Abbr) u)) \to (\forall (a0: C).((csubst1 d u c0 a0) \to
+(\forall (a: C).((drop (S O) d a0 a) \to (ex3_2 T T (\lambda (y1: T).(\lambda
+(_: T).(subst1 d u t4 (lift (S O) d y1)))) (\lambda (_: T).(\lambda (y2:
T).(subst1 d u t0 (lift (S O) d y2)))) (\lambda (y1: T).(\lambda (y2: T).(ty3
g a y1 y2)))))))))))))).(\lambda (e: C).(\lambda (u: T).(\lambda (d:
nat).(\lambda (H4: (getl d c0 (CHead e (Bind Abbr) u))).(\lambda (a0:
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_comm 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_comm (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)
+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:
(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) 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_comm d0 (S O)))) t H1)
+(\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_comm (S O) (minus n (S O)))) (S (plus O (minus n (S O))))
+(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 (c0:
C).(\lambda (u: T).(\lambda (t: T).(\lambda (H0: (ty3 g c0 u t)).(\lambda
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