(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/drop.ma".
+include "basic_1/csuba/drop.ma".
-include "Basic-1/csuba/clear.ma".
+include "basic_1/csuba/clear.ma".
-include "Basic-1/getl/clear.ma".
+include "basic_1/getl/clear.ma".
-theorem csuba_getl_abbr:
+lemma csuba_getl_abbr:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).(\forall
(i: nat).((getl i c1 (CHead d1 (Bind Abbr) u)) \to (\forall (c2: C).((csuba g
c1 c2) \to (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u)))
Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))))) (\lambda (b: B).(\lambda
(H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear (CHead x0
(Bind b) t) (CHead d1 (Bind Abbr) u))).(let H7 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 |
-(CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t)
-(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H8 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 in K
-return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
-\Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t)
-(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H9 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
+C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c]))
+(CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1
+(Bind Abbr) u) t H6)) in ((let H8 \def (f_equal C B (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 with
+[(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead d1 (Bind
Abbr) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u)
-t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda
-(c2: C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda
-(t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def
-(eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abbr
-H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c
-(Bind Abbr) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abbr i c1 d1 u H15
-g c2 H12) in (ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr)
-u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x1:
+t H6)) in ((let H9 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abbr) u)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in
+(\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2:
+C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda (t0:
+T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def (eq_ind_r
+B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abbr H10) in
+(let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind
+Abbr) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abbr i c1 d1 u H15 g c2
+H12) in (ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u)))
+(\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(getl i c2 (CHead
+d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x1:
C).(\lambda (H17: (drop i O c2 (CHead x1 (Bind Abbr) u))).(\lambda (H18:
(csuba g d1 x1)).(ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x1 (getl_intro i c2 (CHead x1
(\lambda (d2: C).(csuba g d1 d2)) x9 (getl_clear_bind x6 c2 x7 x8 H20 (CHead
x9 (Bind Abbr) u) n H22) H23)))) H21)))))))) H17)))))) H14))))))) H11))))))))
i) H7))))) k H3 H4))))))) x H1 H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 2319
-END *)
-theorem csuba_getl_abst:
+lemma csuba_getl_abst:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).(\forall
(i: nat).((getl i c1 (CHead d1 (Bind Abst) u1)) \to (\forall (c2: C).((csuba
g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst)
(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
u2 a))))))))))) (\lambda (b: B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b)
t))).(\lambda (H6: (clear (CHead x0 (Bind b) t) (CHead d1 (Bind Abst)
-u1))).(let H7 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c]))
-(CHead d1 (Bind Abst) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead
-d1 (Bind Abst) u1) t H6)) in ((let H8 \def (f_equal C B (\lambda (e:
-C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abst |
-(CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with
-[(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abst])])) (CHead d1 (Bind
-Abst) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst)
-u1) t H6)) in ((let H9 \def (f_equal C T (\lambda (e: C).(match e in C return
-(\lambda (_: C).T) with [(CSort _) \Rightarrow u1 | (CHead _ _ t0)
-\Rightarrow t0])) (CHead d1 (Bind Abst) u1) (CHead x0 (Bind b) t)
-(clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6)) in (\lambda (H10: (eq B
-Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
-g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
-(Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r B b (\lambda (b0:
-B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abst H10) in (let H15 \def
-(eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind Abst) u1))) H14 d1
-H11) in (let H16 \def (csuba_drop_abst i c1 d1 u1 H15 g c2 H12) in (or_ind
-(ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1))) (\lambda
-(d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
+u1))).(let H7 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abst) u1)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6))
+in ((let H8 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow Abst | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0)
+\Rightarrow b0 | (Flat _) \Rightarrow Abst])])) (CHead d1 (Bind Abst) u1)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6))
+in ((let H9 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u1 | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abst) u1)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6))
+in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2:
+C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda (t0:
+T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r
+B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abst H10) in
+(let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind
+Abst) u1))) H14 d1 H11) in (let H16 \def (csuba_drop_abst i c1 d1 u1 H15 g c2
+H12) in (or_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst)
+u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr)
+u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
+(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
+a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
+a))))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1)))
+(\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
+(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or (ex2 C
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda
+(H17: (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1)))
+(\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop i O c2
+(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C
(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
(_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (H17: (ex2 C (\lambda
-(d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
-d2)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1)))
-(\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
-Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
-d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
-g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-a)))))) (\lambda (x1: C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abst)
-u1))).(\lambda (H19: (csuba g d1 x1)).(or_introl (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x1: C).(\lambda
+(H18: (drop i O c2 (CHead x1 (Bind Abst) u1))).(\lambda (H19: (csuba g d1
+x1)).(or_introl (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst)
+u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2)))))
+(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))
+(ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda
+(d2: C).(csuba g d1 d2)) x1 (getl_intro i c2 (CHead x1 (Bind Abst) u1) (CHead
+x1 (Bind Abst) u1) H18 (clear_bind Abst x1 u1)) H19))))) H17)) (\lambda (H17:
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2
(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x1 (getl_intro i c2
-(CHead x1 (Bind Abst) u1) (CHead x1 (Bind Abst) u1) H18 (clear_bind Abst x1
-u1)) H19))))) H17)) (\lambda (H17: (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
-(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
-C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))).(ex4_3_ind C
-T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2
-(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
-(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
-u2 a)))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1)))
-(\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
-(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
+A).(arity g d2 u2 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x1:
-C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1
-(Bind Abbr) x2))).(\lambda (H19: (csuba g d1 x1)).(\lambda (H20: (arity g d1
-u1 (asucc g x3))).(\lambda (H21: (arity g x1 x2 x3)).(or_intror (ex2 C
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C
(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
(_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
-a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))
-x1 x2 x3 (getl_intro i c2 (CHead x1 (Bind Abbr) x2) (CHead x1 (Bind Abbr) x2)
-H18 (clear_bind Abbr x1 x2)) H19 H20 H21))))))))) H17)) H16)))))))))) H8))
+(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x1: C).(\lambda (x2:
+T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abbr)
+x2))).(\lambda (H19: (csuba g d1 x1)).(\lambda (H20: (arity g d1 u1 (asucc g
+x3))).(\lambda (H21: (arity g x1 x2 x3)).(or_intror (ex2 C (\lambda (d2:
+C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
+g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
+C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x1 x2 x3
+(getl_intro i c2 (CHead x1 (Bind Abbr) x2) (CHead x1 (Bind Abbr) x2) H18
+(clear_bind Abbr x1 x2)) H19 H20 H21))))))))) H17)) H16)))))))))) H8))
H7))))) (\lambda (f: F).(\lambda (H5: (drop i O c1 (CHead x0 (Flat f)
t))).(\lambda (H6: (clear (CHead x0 (Flat f) t) (CHead d1 (Bind Abst)
u1))).(let H7 \def H5 in (unintro C c1 (\lambda (c: C).((drop i O c (CHead x0
c2 x7 x8 H20 (CHead x9 (Bind Abbr) x10) n H23) H24 H25 H26))))))))) H22))
H21)))))))) H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4))))))) x H1
H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 6437
-END *)
-theorem csuba_getl_abst_rev:
+lemma csuba_getl_abst_rev:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).(\forall
(i: nat).((getl i c1 (CHead d1 (Bind Abst) u)) \to (\forall (c2: C).((csuba g
c2 c1) \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))) (\lambda (b:
B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear
(CHead x0 (Bind b) t) (CHead d1 (Bind Abst) u))).(let H7 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abst) u)
-(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in
-((let H8 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_:
-C).B) with [(CSort _) \Rightarrow Abst | (CHead _ k0 _) \Rightarrow (match k0
-in K return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
-\Rightarrow Abst])])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _)
+\Rightarrow c])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in ((let H8 \def
+(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow Abst |
+(CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0) \Rightarrow b0 | (Flat
+_) \Rightarrow Abst])])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
(clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in ((let H9 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
-Abst) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u)
-t H6)) in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda
-(c2: C).(\lambda (H12: (csuba g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda
-(t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def
-(eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abst
-H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c
-(Bind Abst) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abst_rev i c1 d1 u
-H15 g c2 H12) in (or_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead
+_ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in (\lambda (H10: (eq B
+Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
+g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
+(Bind b) t0))) H5 u H9) in (let H14 \def (eq_ind_r B b (\lambda (b0: B).(drop
+i O c1 (CHead x0 (Bind b0) u))) H13 Abst H10) in (let H15 \def (eq_ind_r C x0
+(\lambda (c: C).(drop i O c1 (CHead c (Bind Abst) u))) H14 d1 H11) in (let
+H16 \def (csuba_drop_abst_rev i c1 d1 u H15 g c2 H12) in (or_ind (ex2 C
(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1:
-C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abst) u))).(\lambda (H19:
-(csuba g x1 d1)).(or_introl (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(getl i
-c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x1
-(getl_intro i c2 (CHead x1 (Bind Abst) u) (CHead x1 (Bind Abst) u) H18
-(clear_bind Abst x1 u)) H19))))) H17)) (\lambda (H17: (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2:
-C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1:
-C).(\lambda (x2: T).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Void)
-x2))).(\lambda (H19: (csuba g x1 d1)).(or_intror (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x1 x2 (getl_intro i c2
-(CHead x1 (Bind Void) x2) (CHead x1 (Bind Void) x2) H18 (clear_bind Void x1
-x2)) H19)))))) H17)) H16)))))))))) H8)) H7))))) (\lambda (f: F).(\lambda (H5:
-(drop i O c1 (CHead x0 (Flat f) t))).(\lambda (H6: (clear (CHead x0 (Flat f)
-t) (CHead d1 (Bind Abst) u))).(let H7 \def H5 in (unintro C c1 (\lambda (c:
-C).((drop i O c (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 c)
-\to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop i O
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
+d1)))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))))))) (nat_ind (\lambda (n: nat).(\forall (x1: C).((drop
-n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 x1) \to (or
-(ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl n c2
+T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C (\lambda (d2: C).(drop i O c2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
+(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1: C).(\lambda (H18: (drop
+i O c2 (CHead x1 (Bind Abst) u))).(\lambda (H19: (csuba g x1 d1)).(or_introl
+(ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))))) (\lambda (x1: C).(\lambda (H8: (drop O O x1 (CHead x0 (Flat f)
-t))).(\lambda (c2: C).(\lambda (H9: (csuba g c2 x1)).(let H10 \def (eq_ind C
-x1 (\lambda (c: C).(csuba g c2 c)) H9 (CHead x0 (Flat f) t) (drop_gen_refl x1
-(CHead x0 (Flat f) t) H8)) in (let H_y \def (clear_flat x0 (CHead d1 (Bind
-Abst) u) (clear_gen_flat f x0 (CHead d1 (Bind Abst) u) t H6) f t) in (let H11
-\def (csuba_clear_trans g (CHead x0 (Flat f) t) c2 H10 (CHead d1 (Bind Abst)
-u) H_y) in (ex2_ind C (\lambda (e2: C).(csuba g e2 (CHead d1 (Bind Abst) u)))
-(\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead
-d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (H12:
-(csuba g x2 (CHead d1 (Bind Abst) u))).(\lambda (H13: (clear c2 x2)).(let H_x
-\def (csuba_gen_abst_rev g d1 x2 u H12) in (let H14 \def H_x in (or_ind (ex2
-C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C x2
+d1)))) (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
+(\lambda (d2: C).(csuba g d2 d1)) x1 (getl_intro i c2 (CHead x1 (Bind Abst)
+u) (CHead x1 (Bind Abst) u) H18 (clear_bind Abst x1 u)) H19))))) H17))
+(\lambda (H17: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop i O c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
-(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))) (\lambda (H15: (ex2 C (\lambda (d2: C).(eq C x2 (CHead
-d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda
-(d2: C).(eq C x2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))
-(or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda
-(d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl
-O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
-d2 d1))))) (\lambda (x3: C).(\lambda (H16: (eq C x2 (CHead x3 (Bind Abst)
-u))).(\lambda (H17: (csuba g x3 d1)).(let H18 \def (eq_ind C x2 (\lambda (c:
-C).(clear c2 c)) H13 (CHead x3 (Bind Abst) u) H16) in (or_introl (ex2 C
-(\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2
+d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop i O c2 (CHead
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or
+(ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (ex_intro2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
-(\lambda (d2: C).(csuba g d2 d1)) x3 (getl_intro O c2 (CHead x3 (Bind Abst)
-u) c2 (drop_refl c2) H18) H17)))))) H15)) (\lambda (H15: (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(getl O c2
+d1))))) (\lambda (x1: C).(\lambda (x2: T).(\lambda (H18: (drop i O c2 (CHead
+x1 (Bind Void) x2))).(\lambda (H19: (csuba g x1 d1)).(or_intror (ex2 C
+(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
+d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x1
+x2 (getl_intro i c2 (CHead x1 (Bind Void) x2) (CHead x1 (Bind Void) x2) H18
+(clear_bind Void x1 x2)) H19)))))) H17)) H16)))))))))) H8)) H7))))) (\lambda
+(f: F).(\lambda (H5: (drop i O c1 (CHead x0 (Flat f) t))).(\lambda (H6:
+(clear (CHead x0 (Flat f) t) (CHead d1 (Bind Abst) u))).(let H7 \def H5 in
+(unintro C c1 (\lambda (c: C).((drop i O c (CHead x0 (Flat f) t)) \to
+(\forall (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(getl i c2
(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x3:
-C).(\lambda (x4: T).(\lambda (H16: (eq C x2 (CHead x3 (Bind Void)
-x4))).(\lambda (H17: (csuba g x3 d1)).(let H18 \def (eq_ind C x2 (\lambda (c:
-C).(clear c2 c)) H13 (CHead x3 (Bind Void) x4) H16) in (or_intror (ex2 C
+(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))) (nat_ind (\lambda
+(n: nat).(\forall (x1: C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall
+(c2: C).((csuba g c2 x1) \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(getl n c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1)))))))))) (\lambda (x1: C).(\lambda (H8:
+(drop O O x1 (CHead x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H9: (csuba g
+c2 x1)).(let H10 \def (eq_ind C x1 (\lambda (c: C).(csuba g c2 c)) H9 (CHead
+x0 (Flat f) t) (drop_gen_refl x1 (CHead x0 (Flat f) t) H8)) in (let H_y \def
+(clear_flat x0 (CHead d1 (Bind Abst) u) (clear_gen_flat f x0 (CHead d1 (Bind
+Abst) u) t H6) f t) in (let H11 \def (csuba_clear_trans g (CHead x0 (Flat f)
+t) c2 H10 (CHead d1 (Bind Abst) u) H_y) in (ex2_ind C (\lambda (e2: C).(csuba
+g e2 (CHead d1 (Bind Abst) u))) (\lambda (e2: C).(clear c2 e2)) (or (ex2 C
(\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead
-d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x3
-x4 (getl_intro O c2 (CHead x3 (Bind Void) x4) c2 (drop_refl c2) H18)
-H17))))))) H15)) H14)))))) H11)))))))) (\lambda (n: nat).(\lambda (H8:
-((\forall (x1: C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2:
-C).((csuba g c2 x1) \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl n c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))))))))).(\lambda (x1: C).(\lambda (H9:
-(drop (S n) O x1 (CHead x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H10:
-(csuba g c2 x1)).(let H11 \def (drop_clear x1 (CHead x0 (Flat f) t) n H9) in
-(ex2_3_ind B C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear x1
-(CHead e (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_:
-T).(drop n O e (CHead x0 (Flat f) t))))) (or (ex2 C (\lambda (d2: C).(getl (S
-n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C
-T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x2:
-B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H12: (clear x1 (CHead x3 (Bind
-x2) x4))).(\lambda (H13: (drop n O x3 (CHead x0 (Flat f) t))).(let H14 \def
-(csuba_clear_trans g x1 c2 H10 (CHead x3 (Bind x2) x4) H12) in (ex2_ind C
-(\lambda (e2: C).(csuba g e2 (CHead x3 (Bind x2) x4))) (\lambda (e2:
-C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x5: C).(\lambda (H15: (csuba
-g x5 (CHead x3 (Bind x2) x4))).(\lambda (H16: (clear c2 x5)).(let H_x \def
-(csuba_gen_bind_rev g x2 x3 x5 x4 H15) in (let H17 \def H_x in (ex2_3_ind B C
-T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C x5 (CHead e2 (Bind
-b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2
-x3)))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u)))
+d1))))) (\lambda (x2: C).(\lambda (H12: (csuba g x2 (CHead d1 (Bind Abst)
+u))).(\lambda (H13: (clear c2 x2)).(let H_x \def (csuba_gen_abst_rev g d1 x2
+u H12) in (let H14 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C x2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(eq C x2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2:
+C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H15:
+(ex2 C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
+C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x3:
+C).(\lambda (H16: (eq C x2 (CHead x3 (Bind Abst) u))).(\lambda (H17: (csuba g
+x3 d1)).(let H18 \def (eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13 (CHead
+x3 (Bind Abst) u) H16) in (or_introl (ex2 C (\lambda (d2: C).(getl O c2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda
+(d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
+d1)) x3 (getl_intro O c2 (CHead x3 (Bind Abst) u) c2 (drop_refl c2) H18)
+H17)))))) H15)) (\lambda (H15: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
+T).(eq C x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C
+x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
+d1))) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))) (\lambda (x6: B).(\lambda (x7: C).(\lambda (x8:
-T).(\lambda (H18: (eq C x5 (CHead x7 (Bind x6) x8))).(\lambda (H19: (csuba g
-x7 x3)).(let H20 \def (eq_ind C x5 (\lambda (c: C).(clear c2 c)) H16 (CHead
-x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3 H13 x7 H19) in (or_ind (ex2 C
-(\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl n x7
-(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u)))
+T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (H16: (eq C
+x2 (CHead x3 (Bind Void) x4))).(\lambda (H17: (csuba g x3 d1)).(let H18 \def
+(eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13 (CHead x3 (Bind Void) x4) H16)
+in (or_intror (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))) (\lambda (H22: (ex2 C (\lambda (d2: C).(getl n x7
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
-(\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x9: C).(\lambda (H23: (getl
-n x7 (CHead x9 (Bind Abst) u))).(\lambda (H24: (csuba g x9 d1)).(or_introl
+T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
+T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))) x3 x4 (getl_intro O c2 (CHead x3 (Bind Void) x4) c2
+(drop_refl c2) H18) H17))))))) H15)) H14)))))) H11)))))))) (\lambda (n:
+nat).(\lambda (H8: ((\forall (x1: C).((drop n O x1 (CHead x0 (Flat f) t)) \to
+(\forall (c2: C).((csuba g c2 x1) \to (or (ex2 C (\lambda (d2: C).(getl n c2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl n c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))).(\lambda (x1:
+C).(\lambda (H9: (drop (S n) O x1 (CHead x0 (Flat f) t))).(\lambda (c2:
+C).(\lambda (H10: (csuba g c2 x1)).(let H11 \def (drop_clear x1 (CHead x0
+(Flat f) t) n H9) in (ex2_3_ind B C T (\lambda (b: B).(\lambda (e:
+C).(\lambda (v: T).(clear x1 (CHead e (Bind b) v))))) (\lambda (_:
+B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead x0 (Flat f) t))))) (or
(ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u))) (\lambda
(d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl
(S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba
-g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x9 (getl_clear_bind x6 c2 x7 x8
-H20 (CHead x9 (Bind Abst) u) n H23) H24))))) H22)) (\lambda (H22: (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl n x7 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda
-(d2: C).(\lambda (u2: T).(getl n x7 (CHead d2 (Bind Void) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(getl
-(S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
-C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x9:
-C).(\lambda (x10: T).(\lambda (H23: (getl n x7 (CHead x9 (Bind Void)
-x10))).(\lambda (H24: (csuba g x9 d1)).(or_intror (ex2 C (\lambda (d2:
+g d2 d1))))) (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda
+(H12: (clear x1 (CHead x3 (Bind x2) x4))).(\lambda (H13: (drop n O x3 (CHead
+x0 (Flat f) t))).(let H14 \def (csuba_clear_trans g x1 c2 H10 (CHead x3 (Bind
+x2) x4) H12) in (ex2_ind C (\lambda (e2: C).(csuba g e2 (CHead x3 (Bind x2)
+x4))) (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl (S n)
+c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x5:
+C).(\lambda (H15: (csuba g x5 (CHead x3 (Bind x2) x4))).(\lambda (H16: (clear
+c2 x5)).(let H_x \def (csuba_gen_bind_rev g x2 x3 x5 x4 H15) in (let H17 \def
+H_x in (ex2_3_ind B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
+T).(eq C x5 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csuba g e2 x3)))) (or (ex2 C (\lambda (d2: C).(getl (S n)
+c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x6:
+B).(\lambda (x7: C).(\lambda (x8: T).(\lambda (H18: (eq C x5 (CHead x7 (Bind
+x6) x8))).(\lambda (H19: (csuba g x7 x3)).(let H20 \def (eq_ind C x5 (\lambda
+(c: C).(clear c2 c)) H16 (CHead x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3
+H13 x7 H19) in (or_ind (ex2 C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(getl n x7 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(getl (S n)
+c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H22: (ex2 C
+(\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
C).(getl (S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))
-(ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x9 x10
-(getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Void) x10) n H23) H24))))))
-H22)) H21)))))))) H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4)))))))
-x H1 H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 4703
-END *)
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
+(\lambda (x9: C).(\lambda (H23: (getl n x7 (CHead x9 (Bind Abst)
+u))).(\lambda (H24: (csuba g x9 d1)).(or_introl (ex2 C (\lambda (d2: C).(getl
+(S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
+C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C
+(\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)) x9 (getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Abst)
+u) n H23) H24))))) H22)) (\lambda (H22: (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(getl n x7 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(getl
+n x7 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
+d2 d1))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
+(_: T).(csuba g d2 d1))))) (\lambda (x9: C).(\lambda (x10: T).(\lambda (H23:
+(getl n x7 (CHead x9 (Bind Void) x10))).(\lambda (H24: (csuba g x9
+d1)).(or_intror (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
+(_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
+T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))) x9 x10 (getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind
+Void) x10) n H23) H24)))))) H22)) H21)))))))) H17)))))) H14)))))))
+H11)))))))) i) H7))))) k H3 H4))))))) x H1 H2)))) H0))))))).
-theorem csuba_getl_abbr_rev:
+lemma csuba_getl_abbr_rev:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).(\forall
(i: nat).((getl i c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (c2: C).((csuba
g c2 c1) \to (or3 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr)
(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))) (\lambda (b:
B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear
(CHead x0 (Bind b) t) (CHead d1 (Bind Abbr) u1))).(let H7 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abbr) u1)
-(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6))
-in ((let H8 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda
-(_: C).B) with [(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow
-(match k0 in K return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 |
-(Flat _) \Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b)
-t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in ((let H9 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u1 | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
-Abbr) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr)
-u1) t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1
-x0)).(\lambda (c2: C).(\lambda (H12: (csuba g c2 c1)).(let H13 \def (eq_ind_r
-T t (\lambda (t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u1 H9) in (let
-H14 \def (eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0)
-u1))) H13 Abbr H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O
-c1 (CHead c (Bind Abbr) u1))) H14 d1 H11) in (let H16 \def
-(csuba_drop_abbr_rev i c1 d1 u1 H15 g c2 H12) in (or3_ind (ex2 C (\lambda
-(d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
-d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i
-O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _)
+\Rightarrow c])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in ((let H8 \def
+(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow Abbr |
+(CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0) \Rightarrow b0 | (Flat
+_) \Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in ((let H9 \def
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u1 | (CHead
+_ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in (\lambda (H10: (eq B
+Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
+g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
+(Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r B b (\lambda (b0:
+B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abbr H10) in (let H15 \def
+(eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind Abbr) u1))) H14 d1
+H11) in (let H16 \def (csuba_drop_abbr_rev i c1 d1 u1 H15 g c2 H12) in
+(or3_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1)))
+(\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
+(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2:
+C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
+T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C (\lambda (d2: C).(drop i O c2
+(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
+(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
+C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2)))))
(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C
-(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
-C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1:
+C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abbr) u1))).(\lambda (H19:
+(csuba g x1 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2
+(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst)
+u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
+a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void)
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(getl_intro i c2 (CHead x1 (Bind Abst) x2) (CHead x1 (Bind Abst) x2) H18
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(\lambda (d2: C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2))))
(getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Void) x10) n H23) H24))))))
H22)) H21)))))))) H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4)))))))
x H1 H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 9091
-END *)