(* This file was automatically generated: do not edit *********************)
-set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/sc3/props".
+include "LambdaDelta-1/sc3/defs.ma".
-include "sc3/defs.ma".
+include "LambdaDelta-1/sn3/lift1.ma".
-include "sn3/lift1.ma".
+include "LambdaDelta-1/nf2/lift1.ma".
-include "nf2/lift1.ma".
+include "LambdaDelta-1/csuba/arity.ma".
-include "csuba/arity.ma".
+include "LambdaDelta-1/arity/lift1.ma".
-include "arity/lift1.ma".
+include "LambdaDelta-1/arity/aprem.ma".
-include "arity/aprem.ma".
+include "LambdaDelta-1/llt/props.ma".
-include "llt/props.ma".
+include "LambdaDelta-1/drop1/getl.ma".
-include "drop1/getl.ma".
+include "LambdaDelta-1/drop1/props.ma".
-include "drop1/props.ma".
-
-include "lift1/props.ma".
+include "LambdaDelta-1/lift1/props.ma".
theorem sc3_arity_gen:
\forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a: A).((sc3 g a c
\lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (a: A).(A_ind
(\lambda (a0: A).((sc3 g a0 c t) \to (arity g c t a0))) (\lambda (n:
nat).(\lambda (n0: nat).(\lambda (H: (land (arity g c t (ASort n n0)) (sn3 c
-t))).(let H0 \def H in (and_ind (arity g c t (ASort n n0)) (sn3 c t) (arity g
-c t (ASort n n0)) (\lambda (H1: (arity g c t (ASort n n0))).(\lambda (_: (sn3
-c t)).H1)) H0))))) (\lambda (a0: A).(\lambda (_: (((sc3 g a0 c t) \to (arity
-g c t a0)))).(\lambda (a1: A).(\lambda (_: (((sc3 g a1 c t) \to (arity g c t
-a1)))).(\lambda (H1: (land (arity g c t (AHead a0 a1)) (\forall (d:
+t))).(let H0 \def H in (land_ind (arity g c t (ASort n n0)) (sn3 c t) (arity
+g c t (ASort n n0)) (\lambda (H1: (arity g c t (ASort n n0))).(\lambda (_:
+(sn3 c t)).H1)) H0))))) (\lambda (a0: A).(\lambda (_: (((sc3 g a0 c t) \to
+(arity g c t a0)))).(\lambda (a1: A).(\lambda (_: (((sc3 g a1 c t) \to (arity
+g c t a1)))).(\lambda (H1: (land (arity g c t (AHead a0 a1)) (\forall (d:
C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c)
\to (sc3 g a1 d (THead (Flat Appl) w (lift1 is t)))))))))).(let H2 \def H1 in
-(and_ind (arity g c t (AHead a0 a1)) (\forall (d: C).(\forall (w: T).((sc3 g
+(land_ind (arity g c t (AHead a0 a1)) (\forall (d: C).(\forall (w: T).((sc3 g
a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat
Appl) w (lift1 is t)))))))) (arity g c t (AHead a0 a1)) (\lambda (H3: (arity
g c t (AHead a0 a1))).(\lambda (_: ((\forall (d: C).(\forall (w: T).((sc3 g
c t) \to (\forall (a4: A).((leq g a3 a4) \to (sc3 g a4 c t)))))))))).(\lambda
(c: C).(\lambda (t: T).(\lambda (H0: (land (arity g c t (ASort n n0)) (sn3 c
t))).(\lambda (a3: A).(\lambda (H1: (leq g (ASort n n0) a3)).(let H2 \def H0
-in (and_ind (arity g c t (ASort n n0)) (sn3 c t) (sc3 g a3 c t) (\lambda (H3:
-(arity g c t (ASort n n0))).(\lambda (H4: (sn3 c t)).(let H_y \def
-(arity_repl g c t (ASort n n0) H3 a3 H1) in (let H_x \def (leq_gen_sort g n
+in (land_ind (arity g c t (ASort n n0)) (sn3 c t) (sc3 g a3 c t) (\lambda
+(H3: (arity g c t (ASort n n0))).(\lambda (H4: (sn3 c t)).(let H_y \def
+(arity_repl g c t (ASort n n0) H3 a3 H1) in (let H_x \def (leq_gen_sort1 g n
n0 a3 H1) in (let H5 \def H_x in (ex2_3_ind nat nat nat (\lambda (n2:
-nat).(\lambda (h2: nat).(\lambda (_: nat).(eq A a3 (ASort h2 n2))))) (\lambda
-(n2: nat).(\lambda (h2: nat).(\lambda (k: nat).(eq A (aplus g (ASort n n0) k)
-(aplus g (ASort h2 n2) k))))) (sc3 g a3 c t) (\lambda (x0: nat).(\lambda (x1:
-nat).(\lambda (x2: nat).(\lambda (H6: (eq A a3 (ASort x1 x0))).(\lambda (_:
-(eq A (aplus g (ASort n n0) x2) (aplus g (ASort x1 x0) x2))).(let H8 \def
-(eq_ind A a3 (\lambda (a: A).(arity g c t a)) H_y (ASort x1 x0) H6) in
-(eq_ind_r A (ASort x1 x0) (\lambda (a: A).(sc3 g a c t)) (conj (arity g c t
-(ASort x1 x0)) (sn3 c t) H8 H4) a3 H6))))))) H5)))))) H2)))))))))) (\lambda
-(a: A).(\lambda (_: ((((\forall (a3: A).((llt a3 a) \to (\forall (c:
+nat).(\lambda (h2: nat).(\lambda (k: nat).(eq A (aplus g (ASort n n0) k)
+(aplus g (ASort h2 n2) k))))) (\lambda (n2: nat).(\lambda (h2: nat).(\lambda
+(_: nat).(eq A a3 (ASort h2 n2))))) (sc3 g a3 c t) (\lambda (x0:
+nat).(\lambda (x1: nat).(\lambda (x2: nat).(\lambda (_: (eq A (aplus g (ASort
+n n0) x2) (aplus g (ASort x1 x0) x2))).(\lambda (H7: (eq A a3 (ASort x1
+x0))).(let H8 \def (f_equal A A (\lambda (e: A).e) a3 (ASort x1 x0) H7) in
+(let H9 \def (eq_ind A a3 (\lambda (a: A).(arity g c t a)) H_y (ASort x1 x0)
+H8) in (eq_ind_r A (ASort x1 x0) (\lambda (a: A).(sc3 g a c t)) (conj (arity
+g c t (ASort x1 x0)) (sn3 c t) H9 H4) a3 H8)))))))) H5)))))) H2))))))))))
+(\lambda (a: A).(\lambda (_: ((((\forall (a3: A).((llt a3 a) \to (\forall (c:
C).(\forall (t: T).((sc3 g a3 c t) \to (\forall (a4: A).((leq g a3 a4) \to
(sc3 g a4 c t))))))))) \to (\forall (c: C).(\forall (t: T).((sc3 g a c t) \to
(\forall (a3: A).((leq g a a3) \to (sc3 g a3 c t))))))))).(\lambda (a0:
(AHead a a0)) (\forall (d: C).(\forall (w: T).((sc3 g a d w) \to (\forall
(is: PList).((drop1 is d c) \to (sc3 g a0 d (THead (Flat Appl) w (lift1 is
t)))))))))).(\lambda (a3: A).(\lambda (H3: (leq g (AHead a a0) a3)).(let H4
-\def H2 in (and_ind (arity g c t (AHead a a0)) (\forall (d: C).(\forall (w:
+\def H2 in (land_ind (arity g c t (AHead a a0)) (\forall (d: C).(\forall (w:
T).((sc3 g a d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a0 d
(THead (Flat Appl) w (lift1 is t)))))))) (sc3 g a3 c t) (\lambda (H5: (arity
g c t (AHead a a0))).(\lambda (H6: ((\forall (d: C).(\forall (w: T).((sc3 g a
d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a0 d (THead (Flat
-Appl) w (lift1 is t)))))))))).(let H_x \def (leq_gen_head g a a0 a3 H3) in
-(let H7 \def H_x in (ex3_2_ind A A (\lambda (a4: A).(\lambda (a5: A).(eq A a3
-(AHead a4 a5)))) (\lambda (a4: A).(\lambda (_: A).(leq g a a4))) (\lambda (_:
-A).(\lambda (a5: A).(leq g a0 a5))) (sc3 g a3 c t) (\lambda (x0: A).(\lambda
-(x1: A).(\lambda (H8: (eq A a3 (AHead x0 x1))).(\lambda (H9: (leq g a
-x0)).(\lambda (H10: (leq g a0 x1)).(eq_ind_r A (AHead x0 x1) (\lambda (a4:
-A).(sc3 g a4 c t)) (conj (arity g c t (AHead x0 x1)) (\forall (d: C).(\forall
-(w: T).((sc3 g x0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g x1
-d (THead (Flat Appl) w (lift1 is t)))))))) (arity_repl g c t (AHead a a0) H5
-(AHead x0 x1) (leq_head g a x0 H9 a0 x1 H10)) (\lambda (d: C).(\lambda (w:
-T).(\lambda (H11: (sc3 g x0 d w)).(\lambda (is: PList).(\lambda (H12: (drop1
-is d c)).(H0 (\lambda (a4: A).(\lambda (H13: (llt a4 a0)).(\lambda (c0:
-C).(\lambda (t0: T).(\lambda (H14: (sc3 g a4 c0 t0)).(\lambda (a5:
-A).(\lambda (H15: (leq g a4 a5)).(H1 a4 (llt_trans a4 a0 (AHead a a0) H13
-(llt_head_dx a a0)) c0 t0 H14 a5 H15)))))))) d (THead (Flat Appl) w (lift1 is
-t)) (H6 d w (H1 x0 (llt_repl g a x0 H9 (AHead a a0) (llt_head_sx a a0)) d w
-H11 a (leq_sym g a x0 H9)) is H12) x1 H10))))))) a3 H8)))))) H7)))))
-H4)))))))))))) a2)) a1)).
+Appl) w (lift1 is t)))))))))).(let H_x \def (leq_gen_head1 g a a0 a3 H3) in
+(let H7 \def H_x in (ex3_2_ind A A (\lambda (a4: A).(\lambda (_: A).(leq g a
+a4))) (\lambda (_: A).(\lambda (a5: A).(leq g a0 a5))) (\lambda (a4:
+A).(\lambda (a5: A).(eq A a3 (AHead a4 a5)))) (sc3 g a3 c t) (\lambda (x0:
+A).(\lambda (x1: A).(\lambda (H8: (leq g a x0)).(\lambda (H9: (leq g a0
+x1)).(\lambda (H10: (eq A a3 (AHead x0 x1))).(let H11 \def (f_equal A A
+(\lambda (e: A).e) a3 (AHead x0 x1) H10) in (eq_ind_r A (AHead x0 x1)
+(\lambda (a4: A).(sc3 g a4 c t)) (conj (arity g c t (AHead x0 x1)) (\forall
+(d: C).(\forall (w: T).((sc3 g x0 d w) \to (\forall (is: PList).((drop1 is d
+c) \to (sc3 g x1 d (THead (Flat Appl) w (lift1 is t)))))))) (arity_repl g c t
+(AHead a a0) H5 (AHead x0 x1) (leq_head g a x0 H8 a0 x1 H9)) (\lambda (d:
+C).(\lambda (w: T).(\lambda (H12: (sc3 g x0 d w)).(\lambda (is:
+PList).(\lambda (H13: (drop1 is d c)).(H0 (\lambda (a4: A).(\lambda (H14:
+(llt a4 a0)).(\lambda (c0: C).(\lambda (t0: T).(\lambda (H15: (sc3 g a4 c0
+t0)).(\lambda (a5: A).(\lambda (H16: (leq g a4 a5)).(H1 a4 (llt_trans a4 a0
+(AHead a a0) H14 (llt_head_dx a a0)) c0 t0 H15 a5 H16)))))))) d (THead (Flat
+Appl) w (lift1 is t)) (H6 d w (H1 x0 (llt_repl g a x0 H8 (AHead a a0)
+(llt_head_sx a a0)) d w H12 a (leq_sym g a x0 H8)) is H13) x1 H9))))))) a3
+H11))))))) H7))))) H4)))))))))))) a2)) a1)).
theorem sc3_lift:
\forall (g: G).(\forall (a: A).(\forall (e: C).(\forall (t: T).((sc3 g a e
(\lambda (n: nat).(\lambda (n0: nat).(\lambda (e: C).(\lambda (t: T).(\lambda
(H: (land (arity g e t (ASort n n0)) (sn3 e t))).(\lambda (c: C).(\lambda (h:
nat).(\lambda (d: nat).(\lambda (H0: (drop h d c e)).(let H1 \def H in
-(and_ind (arity g e t (ASort n n0)) (sn3 e t) (land (arity g c (lift h d t)
+(land_ind (arity g e t (ASort n n0)) (sn3 e t) (land (arity g c (lift h d t)
(ASort n n0)) (sn3 c (lift h d t))) (\lambda (H2: (arity g e t (ASort n
n0))).(\lambda (H3: (sn3 e t)).(conj (arity g c (lift h d t) (ASort n n0))
(sn3 c (lift h d t)) (arity_lift g e t (ASort n n0) H2 c h d H0) (sn3_lift e
(d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d
e) \to (sc3 g a1 d (THead (Flat Appl) w (lift1 is t)))))))))).(\lambda (c:
C).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H2: (drop h d c e)).(let H3
-\def H1 in (and_ind (arity g e t (AHead a0 a1)) (\forall (d0: C).(\forall (w:
-T).((sc3 g a0 d0 w) \to (\forall (is: PList).((drop1 is d0 e) \to (sc3 g a1
-d0 (THead (Flat Appl) w (lift1 is t)))))))) (land (arity g c (lift h d t)
+\def H1 in (land_ind (arity g e t (AHead a0 a1)) (\forall (d0: C).(\forall
+(w: T).((sc3 g a0 d0 w) \to (\forall (is: PList).((drop1 is d0 e) \to (sc3 g
+a1 d0 (THead (Flat Appl) w (lift1 is t)))))))) (land (arity g c (lift h d t)
(AHead a0 a1)) (\forall (d0: C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall
(is: PList).((drop1 is d0 c) \to (sc3 g a1 d0 (THead (Flat Appl) w (lift1 is
(lift h d t)))))))))) (\lambda (H4: (arity g e t (AHead a0 a1))).(\lambda
PList).(PList_ind (\lambda (p: PList).(\forall (c: C).(\forall (t: T).((sc3 g
a e t) \to ((drop1 p c e) \to (sc3 g a c (lift1 p t))))))) (\lambda (c:
C).(\lambda (t: T).(\lambda (H: (sc3 g a e t)).(\lambda (H0: (drop1 PNil c
-e)).(let H1 \def (match H0 in drop1 return (\lambda (p: PList).(\lambda (c0:
-C).(\lambda (c1: C).(\lambda (_: (drop1 p c0 c1)).((eq PList p PNil) \to ((eq
-C c0 c) \to ((eq C c1 e) \to (sc3 g a c t)))))))) with [(drop1_nil c0)
-\Rightarrow (\lambda (_: (eq PList PNil PNil)).(\lambda (H2: (eq C c0
-c)).(\lambda (H3: (eq C c0 e)).(eq_ind C c (\lambda (c1: C).((eq C c1 e) \to
-(sc3 g a c t))) (\lambda (H4: (eq C c e)).(eq_ind C e (\lambda (c1: C).(sc3 g
-a c1 t)) H c (sym_eq C c e H4))) c0 (sym_eq C c0 c H2) H3)))) | (drop1_cons
-c1 c2 h d H1 c3 hds0 H2) \Rightarrow (\lambda (H3: (eq PList (PCons h d hds0)
-PNil)).(\lambda (H4: (eq C c1 c)).(\lambda (H5: (eq C c3 e)).((let H6 \def
-(eq_ind PList (PCons h d hds0) (\lambda (e0: PList).(match e0 in PList return
-(\lambda (_: PList).Prop) with [PNil \Rightarrow False | (PCons _ _ _)
-\Rightarrow True])) I PNil H3) in (False_ind ((eq C c1 c) \to ((eq C c3 e)
-\to ((drop h d c1 c2) \to ((drop1 hds0 c2 c3) \to (sc3 g a c t))))) H6)) H4
-H5 H1 H2))))]) in (H1 (refl_equal PList PNil) (refl_equal C c) (refl_equal C
-e))))))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda
-(H: ((\forall (c: C).(\forall (t: T).((sc3 g a e t) \to ((drop1 p c e) \to
-(sc3 g a c (lift1 p t)))))))).(\lambda (c: C).(\lambda (t: T).(\lambda (H0:
-(sc3 g a e t)).(\lambda (H1: (drop1 (PCons n n0 p) c e)).(let H2 \def (match
-H1 in drop1 return (\lambda (p0: PList).(\lambda (c0: C).(\lambda (c1:
-C).(\lambda (_: (drop1 p0 c0 c1)).((eq PList p0 (PCons n n0 p)) \to ((eq C c0
-c) \to ((eq C c1 e) \to (sc3 g a c (lift n n0 (lift1 p t)))))))))) with
-[(drop1_nil c0) \Rightarrow (\lambda (H2: (eq PList PNil (PCons n n0
-p))).(\lambda (H3: (eq C c0 c)).(\lambda (H4: (eq C c0 e)).((let H5 \def
-(eq_ind PList PNil (\lambda (e0: PList).(match e0 in PList return (\lambda
-(_: PList).Prop) with [PNil \Rightarrow True | (PCons _ _ _) \Rightarrow
-False])) I (PCons n n0 p) H2) in (False_ind ((eq C c0 c) \to ((eq C c0 e) \to
-(sc3 g a c (lift n n0 (lift1 p t))))) H5)) H3 H4)))) | (drop1_cons c1 c2 h d
-H2 c3 hds0 H3) \Rightarrow (\lambda (H4: (eq PList (PCons h d hds0) (PCons n
-n0 p))).(\lambda (H5: (eq C c1 c)).(\lambda (H6: (eq C c3 e)).((let H7 \def
-(f_equal PList PList (\lambda (e0: PList).(match e0 in PList return (\lambda
-(_: PList).PList) with [PNil \Rightarrow hds0 | (PCons _ _ p0) \Rightarrow
-p0])) (PCons h d hds0) (PCons n n0 p) H4) in ((let H8 \def (f_equal PList nat
-(\lambda (e0: PList).(match e0 in PList return (\lambda (_: PList).nat) with
-[PNil \Rightarrow d | (PCons _ n1 _) \Rightarrow n1])) (PCons h d hds0)
-(PCons n n0 p) H4) in ((let H9 \def (f_equal PList nat (\lambda (e0:
-PList).(match e0 in PList return (\lambda (_: PList).nat) with [PNil
-\Rightarrow h | (PCons n1 _ _) \Rightarrow n1])) (PCons h d hds0) (PCons n n0
-p) H4) in (eq_ind nat n (\lambda (n1: nat).((eq nat d n0) \to ((eq PList hds0
-p) \to ((eq C c1 c) \to ((eq C c3 e) \to ((drop n1 d c1 c2) \to ((drop1 hds0
-c2 c3) \to (sc3 g a c (lift n n0 (lift1 p t)))))))))) (\lambda (H10: (eq nat
-d n0)).(eq_ind nat n0 (\lambda (n1: nat).((eq PList hds0 p) \to ((eq C c1 c)
-\to ((eq C c3 e) \to ((drop n n1 c1 c2) \to ((drop1 hds0 c2 c3) \to (sc3 g a
-c (lift n n0 (lift1 p t))))))))) (\lambda (H11: (eq PList hds0 p)).(eq_ind
-PList p (\lambda (p0: PList).((eq C c1 c) \to ((eq C c3 e) \to ((drop n n0 c1
-c2) \to ((drop1 p0 c2 c3) \to (sc3 g a c (lift n n0 (lift1 p t))))))))
-(\lambda (H12: (eq C c1 c)).(eq_ind C c (\lambda (c0: C).((eq C c3 e) \to
-((drop n n0 c0 c2) \to ((drop1 p c2 c3) \to (sc3 g a c (lift n n0 (lift1 p
-t))))))) (\lambda (H13: (eq C c3 e)).(eq_ind C e (\lambda (c0: C).((drop n n0
-c c2) \to ((drop1 p c2 c0) \to (sc3 g a c (lift n n0 (lift1 p t))))))
-(\lambda (H14: (drop n n0 c c2)).(\lambda (H15: (drop1 p c2 e)).(sc3_lift g a
-c2 (lift1 p t) (H c2 t H0 H15) c n n0 H14))) c3 (sym_eq C c3 e H13))) c1
-(sym_eq C c1 c H12))) hds0 (sym_eq PList hds0 p H11))) d (sym_eq nat d n0
-H10))) h (sym_eq nat h n H9))) H8)) H7)) H5 H6 H2 H3))))]) in (H2 (refl_equal
-PList (PCons n n0 p)) (refl_equal C c) (refl_equal C e))))))))))) hds)))).
+e)).(let H_y \def (drop1_gen_pnil c e H0) in (eq_ind_r C e (\lambda (c0:
+C).(sc3 g a c0 t)) H c H_y)))))) (\lambda (n: nat).(\lambda (n0:
+nat).(\lambda (p: PList).(\lambda (H: ((\forall (c: C).(\forall (t: T).((sc3
+g a e t) \to ((drop1 p c e) \to (sc3 g a c (lift1 p t)))))))).(\lambda (c:
+C).(\lambda (t: T).(\lambda (H0: (sc3 g a e t)).(\lambda (H1: (drop1 (PCons n
+n0 p) c e)).(let H_x \def (drop1_gen_pcons c e p n n0 H1) in (let H2 \def H_x
+in (ex2_ind C (\lambda (c2: C).(drop n n0 c c2)) (\lambda (c2: C).(drop1 p c2
+e)) (sc3 g a c (lift n n0 (lift1 p t))) (\lambda (x: C).(\lambda (H3: (drop n
+n0 c x)).(\lambda (H4: (drop1 p x e)).(sc3_lift g a x (lift1 p t) (H x t H0
+H4) c n n0 H3)))) H2))))))))))) hds)))).
theorem sc3_abbr:
\forall (g: G).(\forall (a: A).(\forall (vs: TList).(\forall (i:
TList).(\lambda (i: nat).(\lambda (d: C).(\lambda (v: T).(\lambda (c:
C).(\lambda (H: (land (arity g c (THeads (Flat Appl) vs (lift (S i) O v))
(ASort n n0)) (sn3 c (THeads (Flat Appl) vs (lift (S i) O v))))).(\lambda
-(H0: (getl i c (CHead d (Bind Abbr) v))).(let H1 \def H in (and_ind (arity g
+(H0: (getl i c (CHead d (Bind Abbr) v))).(let H1 \def H in (land_ind (arity g
c (THeads (Flat Appl) vs (lift (S i) O v)) (ASort n n0)) (sn3 c (THeads (Flat
Appl) vs (lift (S i) O v))) (land (arity g c (THeads (Flat Appl) vs (TLRef
i)) (ASort n n0)) (sn3 c (THeads (Flat Appl) vs (TLRef i)))) (\lambda (H2:
(lift (S i) O v)) (AHead a0 a1)) (\forall (d0: C).(\forall (w: T).((sc3 g a0
d0 w) \to (\forall (is: PList).((drop1 is d0 c) \to (sc3 g a1 d0 (THead (Flat
Appl) w (lift1 is (THeads (Flat Appl) vs (lift (S i) O v)))))))))))).(\lambda
-(H2: (getl i c (CHead d (Bind Abbr) v))).(let H3 \def H1 in (and_ind (arity g
-c (THeads (Flat Appl) vs (lift (S i) O v)) (AHead a0 a1)) (\forall (d0:
+(H2: (getl i c (CHead d (Bind Abbr) v))).(let H3 \def H1 in (land_ind (arity
+g c (THeads (Flat Appl) vs (lift (S i) O v)) (AHead a0 a1)) (\forall (d0:
C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall (is: PList).((drop1 is d0 c)
\to (sc3 g a1 d0 (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs (lift
(S i) O v)))))))))) (land (arity g c (THeads (Flat Appl) vs (TLRef i)) (AHead
(sn3 c (THeads (Flat Appl) vs (THead (Flat Cast) u t))))))) (\lambda (H1:
(sc3 g (ASort O (next g n0)) c (THeads (Flat Appl) vs u))).(\lambda (H2:
(land (arity g c (THeads (Flat Appl) vs t) (ASort O n0)) (sn3 c (THeads (Flat
-Appl) vs t)))).(let H3 \def H1 in (and_ind (arity g c (THeads (Flat Appl) vs
+Appl) vs t)))).(let H3 \def H1 in (land_ind (arity g c (THeads (Flat Appl) vs
u) (ASort O (next g n0))) (sn3 c (THeads (Flat Appl) vs u)) (land (arity g c
(THeads (Flat Appl) vs (THead (Flat Cast) u t)) (ASort O n0)) (sn3 c (THeads
(Flat Appl) vs (THead (Flat Cast) u t)))) (\lambda (H4: (arity g c (THeads
(Flat Appl) vs u) (ASort O (next g n0)))).(\lambda (H5: (sn3 c (THeads (Flat
-Appl) vs u))).(let H6 \def H2 in (and_ind (arity g c (THeads (Flat Appl) vs
+Appl) vs u))).(let H6 \def H2 in (land_ind (arity g c (THeads (Flat Appl) vs
t) (ASort O n0)) (sn3 c (THeads (Flat Appl) vs t)) (land (arity g c (THeads
(Flat Appl) vs (THead (Flat Cast) u t)) (ASort O n0)) (sn3 c (THeads (Flat
Appl) vs (THead (Flat Cast) u t)))) (\lambda (H7: (arity g c (THeads (Flat
(Flat Appl) vs (THead (Flat Cast) u t)))))))).(\lambda (H1: (sc3 g (ASort n1
n0) c (THeads (Flat Appl) vs u))).(\lambda (H2: (land (arity g c (THeads
(Flat Appl) vs t) (ASort (S n1) n0)) (sn3 c (THeads (Flat Appl) vs t)))).(let
-H3 \def H1 in (and_ind (arity g c (THeads (Flat Appl) vs u) (ASort n1 n0))
+H3 \def H1 in (land_ind (arity g c (THeads (Flat Appl) vs u) (ASort n1 n0))
(sn3 c (THeads (Flat Appl) vs u)) (land (arity g c (THeads (Flat Appl) vs
(THead (Flat Cast) u t)) (ASort (S n1) n0)) (sn3 c (THeads (Flat Appl) vs
(THead (Flat Cast) u t)))) (\lambda (H4: (arity g c (THeads (Flat Appl) vs u)
(ASort n1 n0))).(\lambda (H5: (sn3 c (THeads (Flat Appl) vs u))).(let H6 \def
-H2 in (and_ind (arity g c (THeads (Flat Appl) vs t) (ASort (S n1) n0)) (sn3 c
-(THeads (Flat Appl) vs t)) (land (arity g c (THeads (Flat Appl) vs (THead
+H2 in (land_ind (arity g c (THeads (Flat Appl) vs t) (ASort (S n1) n0)) (sn3
+c (THeads (Flat Appl) vs t)) (land (arity g c (THeads (Flat Appl) vs (THead
(Flat Cast) u t)) (ASort (S n1) n0)) (sn3 c (THeads (Flat Appl) vs (THead
(Flat Cast) u t)))) (\lambda (H7: (arity g c (THeads (Flat Appl) vs t) (ASort
(S n1) n0))).(\lambda (H8: (sn3 c (THeads (Flat Appl) vs t))).(conj (arity g
(arity g c (THeads (Flat Appl) vs t) (AHead a0 a1)) (\forall (d: C).(\forall
(w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1
d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs t))))))))))).(let H3
-\def H1 in (and_ind (arity g c (THeads (Flat Appl) vs u) (AHead a0 (asucc g
+\def H1 in (land_ind (arity g c (THeads (Flat Appl) vs u) (AHead a0 (asucc g
a1))) (\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is:
PList).((drop1 is d c) \to (sc3 g (asucc g a1) d (THead (Flat Appl) w (lift1
is (THeads (Flat Appl) vs u))))))))) (land (arity g c (THeads (Flat Appl) vs
(asucc g a1)))).(\lambda (H5: ((\forall (d: C).(\forall (w: T).((sc3 g a0 d
w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g (asucc g a1) d (THead
(Flat Appl) w (lift1 is (THeads (Flat Appl) vs u))))))))))).(let H6 \def H2
-in (and_ind (arity g c (THeads (Flat Appl) vs t) (AHead a0 a1)) (\forall (d:
+in (land_ind (arity g c (THeads (Flat Appl) vs t) (AHead a0 a1)) (\forall (d:
C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c)
\to (sc3 g a1 d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs
t))))))))) (land (arity g c (THeads (Flat Appl) vs (THead (Flat Cast) u t))
((sns3 c vs) \to (land (arity g c (THeads (Flat Appl) vs (TLRef i)) (ASort n
n0)) (sn3 c (THeads (Flat Appl) vs (TLRef i)))))))))) (\lambda (c:
C).(\lambda (t: T).(\lambda (H: (land (arity g c t (ASort n n0)) (sn3 c
-t))).(let H0 \def H in (and_ind (arity g c t (ASort n n0)) (sn3 c t) (sn3 c
+t))).(let H0 \def H in (land_ind (arity g c t (ASort n n0)) (sn3 c t) (sn3 c
t) (\lambda (_: (arity g c t (ASort n n0))).(\lambda (H2: (sn3 c t)).H2))
H0))))) (\lambda (vs: TList).(\lambda (i: nat).(\lambda (c: C).(\lambda (H:
(arity g c (THeads (Flat Appl) vs (TLRef i)) (ASort n n0))).(\lambda (H0:
(Flat Appl) vs (TLRef i))))))))))))))))) (\lambda (c: C).(\lambda (t:
T).(\lambda (H1: (land (arity g c t (AHead a0 a1)) (\forall (d: C).(\forall
(w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1
-d (THead (Flat Appl) w (lift1 is t)))))))))).(let H2 \def H in (and_ind
+d (THead (Flat Appl) w (lift1 is t)))))))))).(let H2 \def H in (land_ind
(\forall (c0: C).(\forall (t0: T).((sc3 g a0 c0 t0) \to (sn3 c0 t0))))
(\forall (vs: TList).(\forall (i: nat).(\forall (c0: C).((arity g c0 (THeads
(Flat Appl) vs (TLRef i)) a0) \to ((nf2 c0 (TLRef i)) \to ((sns3 c0 vs) \to
t0)))))).(\lambda (H4: ((\forall (vs: TList).(\forall (i: nat).(\forall (c0:
C).((arity g c0 (THeads (Flat Appl) vs (TLRef i)) a0) \to ((nf2 c0 (TLRef i))
\to ((sns3 c0 vs) \to (sc3 g a0 c0 (THeads (Flat Appl) vs (TLRef
-i))))))))))).(let H5 \def H0 in (and_ind (\forall (c0: C).(\forall (t0:
+i))))))))))).(let H5 \def H0 in (land_ind (\forall (c0: C).(\forall (t0:
T).((sc3 g a1 c0 t0) \to (sn3 c0 t0)))) (\forall (vs: TList).(\forall (i:
nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl) vs (TLRef i)) a1) \to
((nf2 c0 (TLRef i)) \to ((sns3 c0 vs) \to (sc3 g a1 c0 (THeads (Flat Appl) vs
T).((sc3 g a1 c0 t0) \to (sn3 c0 t0)))))).(\lambda (_: ((\forall (vs:
TList).(\forall (i: nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl) vs
(TLRef i)) a1) \to ((nf2 c0 (TLRef i)) \to ((sns3 c0 vs) \to (sc3 g a1 c0
-(THeads (Flat Appl) vs (TLRef i))))))))))).(let H8 \def H1 in (and_ind (arity
-g c t (AHead a0 a1)) (\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to
-(\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat Appl) w
+(THeads (Flat Appl) vs (TLRef i))))))))))).(let H8 \def H1 in (land_ind
+(arity g c t (AHead a0 a1)) (\forall (d: C).(\forall (w: T).((sc3 g a0 d w)
+\to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat Appl) w
(lift1 is t)))))))) (sn3 c t) (\lambda (H9: (arity g c t (AHead a0
a1))).(\lambda (H10: ((\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to
(\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat Appl) w
(THead (Flat Appl) (TLRef O) (lift (S x2) O t)) (H_y0 (drop1_cons (CHead x0
(Bind Abst) x1) c (S x2) O (drop_drop (Bind Abst) x2 x0 c H12 x1) c PNil
(drop1_nil c)))) in (let H_x \def (sn3_gen_flat Appl (CHead x0 (Bind Abst)
-x1) (TLRef O) (lift (S x2) O t) H_y1) in (let H14 \def H_x in (and_ind (sn3
+x1) (TLRef O) (lift (S x2) O t) H_y1) in (let H14 \def H_x in (land_ind (sn3
(CHead x0 (Bind Abst) x1) (TLRef O)) (sn3 (CHead x0 (Bind Abst) x1) (lift (S
x2) O t)) (sn3 c t) (\lambda (_: (sn3 (CHead x0 (Bind Abst) x1) (TLRef
O))).(\lambda (H16: (sn3 (CHead x0 (Bind Abst) x1) (lift (S x2) O
\to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat Appl) w
(lift1 is (THeads (Flat Appl) vs (TLRef i)))))))))) H1 (\lambda (d:
C).(\lambda (w: T).(\lambda (H4: (sc3 g a0 d w)).(\lambda (is:
-PList).(\lambda (H5: (drop1 is d c)).(let H6 \def H in (and_ind (\forall (c0:
-C).(\forall (t: T).((sc3 g a0 c0 t) \to (sn3 c0 t)))) (\forall (vs0:
+PList).(\lambda (H5: (drop1 is d c)).(let H6 \def H in (land_ind (\forall
+(c0: C).(\forall (t: T).((sc3 g a0 c0 t) \to (sn3 c0 t)))) (\forall (vs0:
TList).(\forall (i0: nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl)
vs0 (TLRef i0)) a0) \to ((nf2 c0 (TLRef i0)) \to ((sns3 c0 vs0) \to (sc3 g a0
c0 (THeads (Flat Appl) vs0 (TLRef i0))))))))) (sc3 g a1 d (THead (Flat Appl)
((\forall (vs0: TList).(\forall (i0: nat).(\forall (c0: C).((arity g c0
(THeads (Flat Appl) vs0 (TLRef i0)) a0) \to ((nf2 c0 (TLRef i0)) \to ((sns3
c0 vs0) \to (sc3 g a0 c0 (THeads (Flat Appl) vs0 (TLRef i0))))))))))).(let H9
-\def H0 in (and_ind (\forall (c0: C).(\forall (t: T).((sc3 g a1 c0 t) \to
+\def H0 in (land_ind (\forall (c0: C).(\forall (t: T).((sc3 g a1 c0 t) \to
(sn3 c0 t)))) (\forall (vs0: TList).(\forall (i0: nat).(\forall (c0:
C).((arity g c0 (THeads (Flat Appl) vs0 (TLRef i0)) a1) \to ((nf2 c0 (TLRef
i0)) \to ((sns3 c0 vs0) \to (sc3 g a1 c0 (THeads (Flat Appl) vs0 (TLRef
\def
\lambda (g: G).(\lambda (a: A).(\lambda (c: C).(\lambda (t: T).(\lambda (H:
(sc3 g a c t)).(let H_x \def (sc3_props__sc3_sn3_abst g a) in (let H0 \def
-H_x in (and_ind (\forall (c0: C).(\forall (t0: T).((sc3 g a c0 t0) \to (sn3
+H_x in (land_ind (\forall (c0: C).(\forall (t0: T).((sc3 g a c0 t0) \to (sn3
c0 t0)))) (\forall (vs: TList).(\forall (i: nat).(let t0 \def (THeads (Flat
Appl) vs (TLRef i)) in (\forall (c0: C).((arity g c0 t0 a) \to ((nf2 c0
(TLRef i)) \to ((sns3 c0 vs) \to (sc3 g a c0 t0)))))))) (sn3 c t) (\lambda
\lambda (g: G).(\lambda (a: A).(\lambda (vs: TList).(\lambda (c: C).(\lambda
(i: nat).(\lambda (H: (arity g c (THeads (Flat Appl) vs (TLRef i))
a)).(\lambda (H0: (nf2 c (TLRef i))).(\lambda (H1: (sns3 c vs)).(let H_x \def
-(sc3_props__sc3_sn3_abst g a) in (let H2 \def H_x in (and_ind (\forall (c0:
+(sc3_props__sc3_sn3_abst g a) in (let H2 \def H_x in (land_ind (\forall (c0:
C).(\forall (t: T).((sc3 g a c0 t) \to (sn3 c0 t)))) (\forall (vs0:
TList).(\forall (i0: nat).(let t \def (THeads (Flat Appl) vs0 (TLRef i0)) in
(\forall (c0: C).((arity g c0 t a) \to ((nf2 c0 (TLRef i0)) \to ((sns3 c0
T).(\lambda (H0: (land (arity g (CHead c (Bind b) v) (THeads (Flat Appl)
(lifts (S O) O vs) t) (ASort n n0)) (sn3 (CHead c (Bind b) v) (THeads (Flat
Appl) (lifts (S O) O vs) t)))).(\lambda (H1: (sc3 g a1 c v)).(let H2 \def H0
-in (and_ind (arity g (CHead c (Bind b) v) (THeads (Flat Appl) (lifts (S O) O
+in (land_ind (arity g (CHead c (Bind b) v) (THeads (Flat Appl) (lifts (S O) O
vs) t) (ASort n n0)) (sn3 (CHead c (Bind b) v) (THeads (Flat Appl) (lifts (S
O) O vs) t)) (land (arity g c (THeads (Flat Appl) vs (THead (Bind b) v t))
(ASort n n0)) (sn3 c (THeads (Flat Appl) vs (THead (Bind b) v t)))) (\lambda
(lifts (S O) O vs) t) (AHead a a0)) (\forall (d: C).(\forall (w: T).((sc3 g a
d w) \to (\forall (is: PList).((drop1 is d (CHead c (Bind b) v)) \to (sc3 g
a0 d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) (lifts (S O) O vs)
-t))))))))))).(\lambda (H3: (sc3 g a1 c v)).(let H4 \def H2 in (and_ind (arity
-g (CHead c (Bind b) v) (THeads (Flat Appl) (lifts (S O) O vs) t) (AHead a
-a0)) (\forall (d: C).(\forall (w: T).((sc3 g a d w) \to (\forall (is:
+t))))))))))).(\lambda (H3: (sc3 g a1 c v)).(let H4 \def H2 in (land_ind
+(arity g (CHead c (Bind b) v) (THeads (Flat Appl) (lifts (S O) O vs) t)
+(AHead a a0)) (\forall (d: C).(\forall (w: T).((sc3 g a d w) \to (\forall
+(is: PList).((drop1 is d (CHead c (Bind b) v)) \to (sc3 g a0 d (THead (Flat
+Appl) w (lift1 is (THeads (Flat Appl) (lifts (S O) O vs) t))))))))) (land
+(arity g c (THeads (Flat Appl) vs (THead (Bind b) v t)) (AHead a a0))
+(\forall (d: C).(\forall (w: T).((sc3 g a d w) \to (\forall (is:
+PList).((drop1 is d c) \to (sc3 g a0 d (THead (Flat Appl) w (lift1 is (THeads
+(Flat Appl) vs (THead (Bind b) v t))))))))))) (\lambda (H5: (arity g (CHead c
+(Bind b) v) (THeads (Flat Appl) (lifts (S O) O vs) t) (AHead a a0))).(\lambda
+(H6: ((\forall (d: C).(\forall (w: T).((sc3 g a d w) \to (\forall (is:
PList).((drop1 is d (CHead c (Bind b) v)) \to (sc3 g a0 d (THead (Flat Appl)
-w (lift1 is (THeads (Flat Appl) (lifts (S O) O vs) t))))))))) (land (arity g
-c (THeads (Flat Appl) vs (THead (Bind b) v t)) (AHead a a0)) (\forall (d:
+w (lift1 is (THeads (Flat Appl) (lifts (S O) O vs) t))))))))))).(conj (arity
+g c (THeads (Flat Appl) vs (THead (Bind b) v t)) (AHead a a0)) (\forall (d:
C).(\forall (w: T).((sc3 g a d w) \to (\forall (is: PList).((drop1 is d c)
\to (sc3 g a0 d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs (THead
-(Bind b) v t))))))))))) (\lambda (H5: (arity g (CHead c (Bind b) v) (THeads
-(Flat Appl) (lifts (S O) O vs) t) (AHead a a0))).(\lambda (H6: ((\forall (d:
-C).(\forall (w: T).((sc3 g a d w) \to (\forall (is: PList).((drop1 is d
-(CHead c (Bind b) v)) \to (sc3 g a0 d (THead (Flat Appl) w (lift1 is (THeads
-(Flat Appl) (lifts (S O) O vs) t))))))))))).(conj (arity g c (THeads (Flat
-Appl) vs (THead (Bind b) v t)) (AHead a a0)) (\forall (d: C).(\forall (w:
-T).((sc3 g a d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a0 d
-(THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs (THead (Bind b) v
-t)))))))))) (arity_appls_bind g b H c v a1 (sc3_arity_gen g c v a1 H3) t vs
-(AHead a a0) H5) (\lambda (d: C).(\lambda (w: T).(\lambda (H7: (sc3 g a d
-w)).(\lambda (is: PList).(\lambda (H8: (drop1 is d c)).(let H_y \def (H1
-(TCons w (lifts1 is vs))) in (eq_ind_r T (THeads (Flat Appl) (lifts1 is vs)
-(lift1 is (THead (Bind b) v t))) (\lambda (t0: T).(sc3 g a0 d (THead (Flat
-Appl) w t0))) (eq_ind_r T (THead (Bind b) (lift1 is v) (lift1 (Ss is) t))
-(\lambda (t0: T).(sc3 g a0 d (THead (Flat Appl) w (THeads (Flat Appl) (lifts1
-is vs) t0)))) (H_y d (lift1 is v) (lift1 (Ss is) t) (eq_ind TList (lifts1 (Ss
-is) (lifts (S O) O vs)) (\lambda (t0: TList).(sc3 g a0 (CHead d (Bind b)
-(lift1 is v)) (THead (Flat Appl) (lift (S O) O w) (THeads (Flat Appl) t0
-(lift1 (Ss is) t))))) (eq_ind T (lift1 (Ss is) (THeads (Flat Appl) (lifts (S
-O) O vs) t)) (\lambda (t0: T).(sc3 g a0 (CHead d (Bind b) (lift1 is v))
-(THead (Flat Appl) (lift (S O) O w) t0))) (H6 (CHead d (Bind b) (lift1 is v))
-(lift (S O) O w) (sc3_lift g a d w H7 (CHead d (Bind b) (lift1 is v)) (S O) O
-(drop_drop (Bind b) O d d (drop_refl d) (lift1 is v))) (Ss is)
+(Bind b) v t)))))))))) (arity_appls_bind g b H c v a1 (sc3_arity_gen g c v a1
+H3) t vs (AHead a a0) H5) (\lambda (d: C).(\lambda (w: T).(\lambda (H7: (sc3
+g a d w)).(\lambda (is: PList).(\lambda (H8: (drop1 is d c)).(let H_y \def
+(H1 (TCons w (lifts1 is vs))) in (eq_ind_r T (THeads (Flat Appl) (lifts1 is
+vs) (lift1 is (THead (Bind b) v t))) (\lambda (t0: T).(sc3 g a0 d (THead
+(Flat Appl) w t0))) (eq_ind_r T (THead (Bind b) (lift1 is v) (lift1 (Ss is)
+t)) (\lambda (t0: T).(sc3 g a0 d (THead (Flat Appl) w (THeads (Flat Appl)
+(lifts1 is vs) t0)))) (H_y d (lift1 is v) (lift1 (Ss is) t) (eq_ind TList
+(lifts1 (Ss is) (lifts (S O) O vs)) (\lambda (t0: TList).(sc3 g a0 (CHead d
+(Bind b) (lift1 is v)) (THead (Flat Appl) (lift (S O) O w) (THeads (Flat
+Appl) t0 (lift1 (Ss is) t))))) (eq_ind T (lift1 (Ss is) (THeads (Flat Appl)
+(lifts (S O) O vs) t)) (\lambda (t0: T).(sc3 g a0 (CHead d (Bind b) (lift1 is
+v)) (THead (Flat Appl) (lift (S O) O w) t0))) (H6 (CHead d (Bind b) (lift1 is
+v)) (lift (S O) O w) (sc3_lift g a d w H7 (CHead d (Bind b) (lift1 is v)) (S
+O) O (drop_drop (Bind b) O d d (drop_refl d) (lift1 is v))) (Ss is)
(drop1_skip_bind b c is d v H8)) (THeads (Flat Appl) (lifts1 (Ss is) (lifts
(S O) O vs)) (lift1 (Ss is) t)) (lifts1_flat Appl (Ss is) t (lifts (S O) O
vs))) (lifts (S O) O (lifts1 is vs)) (lifts1_xhg is vs)) (sc3_lift1 g c a1 is
T).(\lambda (t: T).(\lambda (H: (land (arity g c (THeads (Flat Appl) vs
(THead (Bind Abbr) v t)) (ASort n n0)) (sn3 c (THeads (Flat Appl) vs (THead
(Bind Abbr) v t))))).(\lambda (H0: (sc3 g a1 c v)).(\lambda (w: T).(\lambda
-(H1: (sc3 g (asucc g a1) c w)).(let H2 \def H in (and_ind (arity g c (THeads
+(H1: (sc3 g (asucc g a1) c w)).(let H2 \def H in (land_ind (arity g c (THeads
(Flat Appl) vs (THead (Bind Abbr) v t)) (ASort n n0)) (sn3 c (THeads (Flat
Appl) vs (THead (Bind Abbr) v t))) (land (arity g c (THeads (Flat Appl) vs
(THead (Flat Appl) v (THead (Bind Abst) w t))) (ASort n n0)) (sn3 c (THeads
PList).((drop1 is d c) \to (sc3 g a0 d (THead (Flat Appl) w (lift1 is (THeads
(Flat Appl) vs (THead (Bind Abbr) v t)))))))))))).(\lambda (H2: (sc3 g a1 c
v)).(\lambda (w: T).(\lambda (H3: (sc3 g (asucc g a1) c w)).(let H4 \def H1
-in (and_ind (arity g c (THeads (Flat Appl) vs (THead (Bind Abbr) v t)) (AHead
-a a0)) (\forall (d: C).(\forall (w0: T).((sc3 g a d w0) \to (\forall (is:
-PList).((drop1 is d c) \to (sc3 g a0 d (THead (Flat Appl) w0 (lift1 is
+in (land_ind (arity g c (THeads (Flat Appl) vs (THead (Bind Abbr) v t))
+(AHead a a0)) (\forall (d: C).(\forall (w0: T).((sc3 g a d w0) \to (\forall
+(is: PList).((drop1 is d c) \to (sc3 g a0 d (THead (Flat Appl) w0 (lift1 is
(THeads (Flat Appl) vs (THead (Bind Abbr) v t)))))))))) (land (arity g c
(THeads (Flat Appl) vs (THead (Flat Appl) v (THead (Bind Abst) w t))) (AHead
a a0)) (\forall (d: C).(\forall (w0: T).((sc3 g a d w0) \to (\forall (is:
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