- some bugs fixed in the domain-based preorders on environments

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / csuba / drop.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csuba/drop.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csuba/drop.ma
index 4d965603c5ec926efdad85c1cefcc968ae40bbea..6b30e0e1b69615bd3b7ac2261201e5ed140be9cd 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csuba/drop.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csuba/drop.ma
@@ -14,9 +14,9 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "csuba/fwd.ma".
+include "LambdaDelta-1/csuba/fwd.ma".
 
-include "drop/fwd.ma".
+include "LambdaDelta-1/drop/fwd.ma".
 
 theorem csuba_drop_abbr:
  \forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop i 
@@ -54,18 +54,13 @@ O (CSort n0) (CHead d1 (Bind Abbr) u))).(\lambda (g: G).(\lambda (c2:
 C).(\lambda (_: (csuba g (CSort n0) c2)).(and3_ind (eq C (CHead d1 (Bind 
 Abbr) u) (CSort n0)) (eq nat (S n) O) (eq nat O O) (ex2 C (\lambda (d2: 
 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 
-d2))) (\lambda (H2: (eq C (CHead d1 (Bind Abbr) u) (CSort n0))).(\lambda (_: 
-(eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (match H2 in eq 
-return (\lambda (c: C).(\lambda (_: (eq ? ? c)).((eq C c (CSort n0)) \to (ex2 
-C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: 
-C).(csuba g d1 d2)))))) with [refl_equal \Rightarrow (\lambda (H5: (eq C 
-(CHead d1 (Bind Abbr) u) (CSort n0))).(let H6 \def (eq_ind C (CHead d1 (Bind 
-Abbr) u) (\lambda (e: C).(match e in C return (\lambda (_: C).Prop) with 
-[(CSort _) \Rightarrow False | (CHead _ _ _) \Rightarrow True])) I (CSort n0) 
-H5) in (False_ind (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind 
-Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H6)))]) in (H5 (refl_equal C 
-(CSort n0))))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abbr) u) 
-H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u: 
+d2))) (\lambda (_: (eq C (CHead d1 (Bind Abbr) u) (CSort n0))).(\lambda (H3: 
+(eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S n) 
+(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O 
+\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (ex2 C 
+(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: 
+C).(csuba g d1 d2))) H5))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abbr) 
+u) H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u: 
 T).((drop (S n) O c (CHead d1 (Bind Abbr) u)) \to (\forall (g: G).(\forall 
 (c2: C).((csuba g c c2) \to (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead 
 d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))))))))))).(\lambda (k: 
@@ -152,41 +147,42 @@ Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Bind Abbr) n x0
 (CHead x (Bind Abbr) u) H17 x1) H15)))))) H13)) c2 H9)))))))) H8)) H7))))) 
 (\lambda (H5: (csuba g (CHead c (Bind Void) t) c2)).(\lambda (H6: (drop (r 
 (Bind Void) n) O c (CHead d1 (Bind Abbr) u))).(let H_x \def (csuba_gen_void g 
-c c2 t H5) in (let H7 \def H_x in (ex2_ind C (\lambda (d2: C).(eq C c2 (CHead 
-d2 (Bind Void) t))) (\lambda (d2: C).(csuba g c d2)) (ex2 C (\lambda (d2: 
+c c2 t H5) in (let H7 \def H_x in (ex2_3_ind B C T (\lambda (b0: B).(\lambda 
+(d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b0) u2))))) (\lambda (_: 
+B).(\lambda (d2: C).(\lambda (_: T).(csuba g c d2)))) (ex2 C (\lambda (d2: 
 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 
-d2))) (\lambda (x: C).(\lambda (H8: (eq C c2 (CHead x (Bind Void) 
-t))).(\lambda (H9: (csuba g c x)).(eq_ind_r C (CHead x (Bind Void) t) 
+d2))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H8: (eq C 
+c2 (CHead x1 (Bind x0) x2))).(\lambda (H9: (csuba g c x1)).(eq_ind_r C (CHead 
+x1 (Bind x0) x2) (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 
+(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H10 \def 
+(H c d1 u H6 g x1 H9) in (ex2_ind C (\lambda (d2: C).(drop n O x1 (CHead d2 
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abbr) u))) (\lambda 
+(d2: C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H11: (drop n O x1 (CHead 
+x (Bind Abbr) u))).(\lambda (H12: (csuba g d1 x)).(let H13 \def (refl_equal 
+nat (r (Bind Abbr) n)) in (let H14 \def (eq_ind nat n (\lambda (n0: 
+nat).(drop n0 O x1 (CHead x (Bind Abbr) u))) H11 (r (Bind Abbr) n) H13) in 
+(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Bind x0) n 
+x1 (CHead x (Bind Abbr) u) H14 x2) H12)))))) H10)) c2 H8)))))) H7))))) b H3 
+H4)))) (\lambda (f: F).(\lambda (H3: (csuba g (CHead c (Flat f) t) 
+c2)).(\lambda (H4: (drop (r (Flat f) n) O c (CHead d1 (Bind Abbr) u))).(let 
+H_x \def (csuba_gen_flat g c c2 t f H3) in (let H5 \def H_x in (ex2_2_ind C T 
+(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g c d2))) (ex2 C (\lambda (d2: C).(drop (S n) 
+O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda 
+(x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0 (Flat f) 
+x1))).(\lambda (H7: (csuba g c x0)).(eq_ind_r C (CHead x0 (Flat f) x1) 
 (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind 
-Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H10 \def (H c d1 u H6 g x 
-H9) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u))) 
-(\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O 
-(CHead x (Bind Void) t) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g 
-d1 d2))) (\lambda (x0: C).(\lambda (H11: (drop n O x (CHead x0 (Bind Abbr) 
-u))).(\lambda (H12: (csuba g d1 x0)).(let H13 \def (refl_equal nat (r (Bind 
-Abbr) n)) in (let H14 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x 
-(CHead x0 (Bind Abbr) u))) H11 (r (Bind Abbr) n) H13) in (ex_intro2 C 
-(\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr) 
-u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Void) n x (CHead 
-x0 (Bind Abbr) u) H14 t) H12)))))) H10)) c2 H8)))) H7))))) b H3 H4)))) 
-(\lambda (f: F).(\lambda (H3: (csuba g (CHead c (Flat f) t) c2)).(\lambda 
-(H4: (drop (r (Flat f) n) O c (CHead d1 (Bind Abbr) u))).(let H_x \def 
-(csuba_gen_flat g c c2 t f H3) in (let H5 \def H_x in (ex2_2_ind C T (\lambda 
-(d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: 
-C).(\lambda (_: T).(csuba g c d2))) (ex2 C (\lambda (d2: C).(drop (S n) O c2 
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x0: 
-C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0 (Flat f) x1))).(\lambda 
-(H7: (csuba g c x0)).(eq_ind_r C (CHead x0 (Flat f) x1) (\lambda (c0: C).(ex2 
-C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind Abbr) u))) (\lambda (d2: 
-C).(csuba g d1 d2)))) (let H8 \def (H0 d1 u H4 g x0 H7) in (ex2_ind C 
-(\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abbr) u))) (\lambda (d2: 
-C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) 
-x1) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda 
-(x: C).(\lambda (H9: (drop (S n) O x0 (CHead x (Bind Abbr) u))).(\lambda 
-(H10: (csuba g d1 x)).(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
-(Flat f) x1) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x 
-(drop_drop (Flat f) n x0 (CHead x (Bind Abbr) u) H9 x1) H10)))) H8)) c2 
-H6))))) H5)))))) k H2 (drop_gen_drop k c (CHead d1 (Bind Abbr) u) t n 
+Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H8 \def (H0 d1 u H4 g x0 
+H7) in (ex2_ind C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abbr) 
+u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O 
+(CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g 
+d1 d2))) (\lambda (x: C).(\lambda (H9: (drop (S n) O x0 (CHead x (Bind Abbr) 
+u))).(\lambda (H10: (csuba g d1 x)).(ex_intro2 C (\lambda (d2: C).(drop (S n) 
+O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g 
+d1 d2)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abbr) u) H9 x1) H10)))) 
+H8)) c2 H6))))) H5)))))) k H2 (drop_gen_drop k c (CHead d1 (Bind Abbr) u) t n 
 H1)))))))))))) c1)))) i).
 
 theorem csuba_drop_abst:
@@ -313,112 +309,103 @@ C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) 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 (H2: (eq C (CHead d1 (Bind Abst) u1) (CSort n0))).(\lambda 
-(_: (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (match H2 in eq 
-return (\lambda (c: C).(\lambda (_: (eq ? ? c)).((eq C c (CSort n0)) \to (or 
-(ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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))))))))) with 
-[refl_equal \Rightarrow (\lambda (H5: (eq C (CHead d1 (Bind Abst) u1) (CSort 
-n0))).(let H6 \def (eq_ind C (CHead d1 (Bind Abst) u1) (\lambda (e: C).(match 
-e in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | 
-(CHead _ _ _) \Rightarrow True])) I (CSort n0) H5) in (False_ind (or (ex2 C 
-(\lambda (d2: C).(drop (S n) 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 (S n) 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)))))) H6)))]) in 
-(H5 (refl_equal C (CSort n0))))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind 
-Abst) u1) H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: 
-C).(\forall (u1: T).((drop (S n) O c (CHead d1 (Bind Abst) u1)) \to (\forall 
-(g: G).(\forall (c2: C).((csuba g c c2) \to (or (ex2 C (\lambda (d2: C).(drop 
-(S n) 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 (S n) 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 (k: K).(\lambda (t: 
-T).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H1: (drop (S n) O (CHead c k 
-t) (CHead d1 (Bind Abst) u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H2: 
-(csuba g (CHead c k t) c2)).(K_ind (\lambda (k0: K).((csuba g (CHead c k0 t) 
-c2) \to ((drop (r k0 n) O c (CHead d1 (Bind Abst) u1)) \to (or (ex2 C 
-(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: 
+a)))))) (\lambda (_: (eq C (CHead d1 (Bind Abst) u1) (CSort n0))).(\lambda 
+(H3: (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S 
+n) (\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O 
+\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2 
+C (\lambda (d2: C).(drop (S n) 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 (S n) 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 
-(b: B).(\lambda (H3: (csuba g (CHead c (Bind b) t) c2)).(\lambda (H4: (drop 
-(r (Bind b) n) O c (CHead d1 (Bind Abst) u1))).(B_ind (\lambda (b0: 
-B).((csuba g (CHead c (Bind b0) t) c2) \to ((drop (r (Bind b0) n) O c (CHead 
-d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (H5: (csuba g (CHead c (Bind Abbr) t) c2)).(\lambda (H6: 
-(drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abst) u1))).(let H_x \def 
-(csuba_gen_abbr g c c2 t H5) in (let H7 \def H_x in (ex2_ind C (\lambda (d2: 
-C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba g c d2)) (or 
-(ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (x: 
-C).(\lambda (H8: (eq C c2 (CHead x (Bind Abbr) t))).(\lambda (H9: (csuba g c 
-x)).(eq_ind_r C (CHead x (Bind Abbr) t) (\lambda (c0: C).(or (ex2 C (\lambda 
-(d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H10 \def (H c d1 u1 H6 g 
-x H9) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (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 n O x (CHead d2 (Bind Abbr) u2))))) 
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) H5))))) 
+(drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u1) H0))))))))) (\lambda (c: 
+C).(\lambda (H0: ((\forall (d1: C).(\forall (u1: T).((drop (S n) O c (CHead 
+d1 (Bind Abst) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c c2) \to 
+(or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 
+a)))))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda 
+(u1: T).(\lambda (H1: (drop (S n) O (CHead c k t) (CHead d1 (Bind Abst) 
+u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H2: (csuba g (CHead c k t) 
+c2)).(K_ind (\lambda (k0: K).((csuba g (CHead c k0 t) c2) \to ((drop (r k0 n) 
+O c (CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (b: B).(\lambda (H3: (csuba g (CHead c 
+(Bind b) t) c2)).(\lambda (H4: (drop (r (Bind b) n) O c (CHead d1 (Bind Abst) 
+u1))).(B_ind (\lambda (b0: B).((csuba g (CHead c (Bind b0) t) c2) \to ((drop 
+(r (Bind b0) n) O c (CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: 
+C).(drop (S n) 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 (S 
+n) 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 (H5: (csuba g 
+(CHead c (Bind Abbr) t) c2)).(\lambda (H6: (drop (r (Bind Abbr) n) O c (CHead 
+d1 (Bind Abst) u1))).(let H_x \def (csuba_gen_abbr g c c2 t H5) in (let H7 
+\def H_x in (ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) 
+(\lambda (d2: C).(csuba g c d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (x: C).(\lambda (H8: (eq C c2 (CHead x (Bind Abbr) 
+t))).(\lambda (H9: (csuba g c x)).(eq_ind_r C (CHead x (Bind Abbr) t) 
+(\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (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 (S n) O (CHead x (Bind Abbr) t) 
+C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c0 (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))))))) (let H10 \def (H c d1 u1 H6 g x H9) in (or_ind (ex2 C (\lambda (d2: 
+C).(drop n O x (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 n O x 
 (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 (H11: (ex2 C (\lambda (d2: C).(drop n O x 
-(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C 
-(\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u1))) (\lambda (d2: 
-C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind 
-Abbr) t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) 
+A).(arity g d2 u2 a))))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x 
+(Bind Abbr) t) (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 (S n) O 
 (CHead x (Bind Abbr) t) (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 (x0: 
-C).(\lambda (H12: (drop n O x (CHead x0 (Bind Abst) u1))).(\lambda (H13: 
-(csuba g d1 x0)).(let H14 \def (refl_equal nat (r (Bind Abbr) n)) in (let H15 
-\def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abst) 
-u1))) H12 (r (Bind Abbr) n) H14) in (or_introl (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u2))))) 
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda 
+(H11: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u1))) 
+(\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop n O x 
+(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) 
+(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 (x0: C).(\lambda (H12: (drop n O x (CHead 
+x0 (Bind Abst) u1))).(\lambda (H13: (csuba g d1 x0)).(let H14 \def 
+(refl_equal nat (r (Bind Abbr) n)) in (let H15 \def (eq_ind nat n (\lambda 
+(n0: nat).(drop n0 O x (CHead x0 (Bind Abst) u1))) H12 (r (Bind Abbr) n) H14) 
+in (or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) 
+(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 (S n) O (CHead x 
+(Bind Abbr) t) (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).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u1))) (\lambda 
+(d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abbr) n x (CHead x0 (Bind Abst) 
+u1) H15 t) H13))))))) H11)) (\lambda (H11: (ex4_3 C T A (\lambda (d2: 
+C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (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).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abbr) 
-n x (CHead x0 (Bind Abst) u1) H15 t) H13))))))) H11)) (\lambda (H11: (ex4_3 C 
-T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (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 (_: 
+(\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 n O x (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 
@@ -642,147 +629,149 @@ C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
 H18))))))))))) H14)) H13)) c2 H9)))))))) H8)) H7))))) (\lambda (H5: (csuba g 
 (CHead c (Bind Void) t) c2)).(\lambda (H6: (drop (r (Bind Void) n) O c (CHead 
 d1 (Bind Abst) u1))).(let H_x \def (csuba_gen_void g c c2 t H5) in (let H7 
-\def H_x in (ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Void) t))) 
-(\lambda (d2: C).(csuba g c d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (x: C).(\lambda (H8: (eq C c2 (CHead x (Bind Void) 
-t))).(\lambda (H9: (csuba g c x)).(eq_ind_r C (CHead x (Bind Void) t) 
-(\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H10 \def (H c d1 u1 H6 g x H9) in (or_ind (ex2 C (\lambda (d2: 
-C).(drop n O x (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 n O x 
-(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: 
+\def H_x in (ex2_3_ind B C T (\lambda (b0: B).(\lambda (d2: C).(\lambda (u2: 
+T).(eq C c2 (CHead d2 (Bind b0) u2))))) (\lambda (_: B).(\lambda (d2: 
+C).(\lambda (_: T).(csuba g c d2)))) (or (ex2 C (\lambda (d2: C).(drop (S n) 
+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 (S n) 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).(drop (S n) O (CHead x 
-(Bind Void) t) (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 (S n) O 
-(CHead x (Bind Void) t) (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 
-(H11: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u1))) 
-(\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop n O x 
-(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C 
-(\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) 
+A).(arity g d2 u2 a)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: 
+T).(\lambda (H8: (eq C c2 (CHead x1 (Bind x0) x2))).(\lambda (H9: (csuba g c 
+x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c0: C).(or (ex2 C (\lambda 
+(d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H10 \def (H c d1 u1 H6 g 
+x1 H9) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x1 (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 (S n) O (CHead x (Bind Void) t) 
-(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 (x0: C).(\lambda (H12: (drop n O x (CHead 
-x0 (Bind Abst) u1))).(\lambda (H13: (csuba g d1 x0)).(let H14 \def 
-(refl_equal nat (r (Bind Abbr) n)) in (let H15 \def (eq_ind nat n (\lambda 
-(n0: nat).(drop n0 O x (CHead x0 (Bind Abst) u1))) H12 (r (Bind Abbr) n) H14) 
-in (or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) 
+C).(\lambda (u2: T).(\lambda (_: A).(drop n O x1 (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).(drop (S n) O (CHead x1 (Bind x0) x2) 
 (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 (S n) O (CHead x 
-(Bind Void) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x1 
+(Bind x0) x2) (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).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u1))) (\lambda 
-(d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Void) n x (CHead x0 (Bind Abst) 
-u1) H15 t) H13))))))) H11)) (\lambda (H11: (ex4_3 C T A (\lambda (d2: 
-C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (CHead d2 (Bind Abbr) u2))))) 
+(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (H11: (ex2 C (\lambda 
+(d2: C).(drop n O x1 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 
+d2)))).(ex2_ind C (\lambda (d2: C).(drop n O x1 (CHead d2 (Bind Abst) u1))) 
+(\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) O 
+(CHead x1 (Bind x0) x2) (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 
+(S n) O (CHead x1 (Bind x0) x2) (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 (x: 
+C).(\lambda (H12: (drop n O x1 (CHead x (Bind Abst) u1))).(\lambda (H13: 
+(csuba g d1 x)).(let H14 \def (refl_equal nat (r (Bind Abbr) n)) in (let H15 
+\def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x1 (CHead x (Bind Abst) 
+u1))) H12 (r (Bind Abbr) n) H14) in (or_introl (ex2 C (\lambda (d2: C).(drop 
+(S n) O (CHead x1 (Bind x0) x2) (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 (S n) O (CHead x1 (Bind x0) x2) (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 n O x (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) 
+(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 
+(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Bind x0) n 
+x1 (CHead x (Bind Abst) u1) H15 x2) H13))))))) H11)) (\lambda (H11: (ex4_3 C 
+T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x1 (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 n O x1 (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).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u1))) (\lambda 
+C).(drop (S n) O (CHead x1 (Bind x0) x2) (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 (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind 
+T).(\lambda (_: A).(drop (S n) O (CHead x1 (Bind x0) x2) (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 (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H12: 
-(drop n O x (CHead x0 (Bind Abbr) x1))).(\lambda (H13: (csuba g d1 
-x0)).(\lambda (H14: (arity g d1 u1 (asucc g x2))).(\lambda (H15: (arity g x0 
-x1 x2)).(let H16 \def (refl_equal nat (r (Bind Abbr) n)) in (let H17 \def 
-(eq_ind nat n (\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abbr) x1))) H12 
-(r (Bind Abbr) n) H16) in (or_intror (ex2 C (\lambda (d2: C).(drop (S n) O 
-(CHead x (Bind Void) t) (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 
-(S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: 
+a)))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: A).(\lambda (H12: 
+(drop n O x1 (CHead x3 (Bind Abbr) x4))).(\lambda (H13: (csuba g d1 
+x3)).(\lambda (H14: (arity g d1 u1 (asucc g x5))).(\lambda (H15: (arity g x3 
+x4 x5)).(let H16 \def (refl_equal nat (r (Bind Abbr) n)) in (let H17 \def 
+(eq_ind nat n (\lambda (n0: nat).(drop n0 O x1 (CHead x3 (Bind Abbr) x4))) 
+H12 (r (Bind Abbr) n) H16) in (or_intror (ex2 C (\lambda (d2: C).(drop (S n) 
+O (CHead x1 (Bind x0) x2) (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 (S n) O (CHead x1 (Bind x0) x2) (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).(drop (S 
+n) O (CHead x1 (Bind x0) x2) (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).(drop (S n) O (CHead x 
-(Bind Void) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: 
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x3 x4 x5 
+(drop_drop (Bind x0) n x1 (CHead x3 (Bind Abbr) x4) H17 x2) H13 H14 
+H15))))))))))) H11)) H10)) c2 H8)))))) H7))))) b H3 H4)))) (\lambda (f: 
+F).(\lambda (H3: (csuba g (CHead c (Flat f) t) c2)).(\lambda (H4: (drop (r 
+(Flat f) n) O c (CHead d1 (Bind Abst) u1))).(let H_x \def (csuba_gen_flat g c 
+c2 t f H3) in (let H5 \def H_x in (ex2_2_ind C T (\lambda (d2: C).(\lambda 
+(u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g c d2))) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0 
+(Flat f) x1))).(\lambda (H7: (csuba g c x0)).(eq_ind_r C (CHead x0 (Flat f) 
+x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H8 \def (H0 d1 u1 H4 g x0 H7) in (or_ind (ex2 C (\lambda (d2: 
+C).(drop (S n) O x0 (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 (S 
+n) O x0 (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)))) x0 x1 x2 (drop_drop (Bind Void) 
-n x (CHead x0 (Bind Abbr) x1) H17 t) H13 H14 H15))))))))))) H11)) H10)) c2 
-H8)))) H7))))) b H3 H4)))) (\lambda (f: F).(\lambda (H3: (csuba g (CHead c 
-(Flat f) t) c2)).(\lambda (H4: (drop (r (Flat f) n) O c (CHead d1 (Bind Abst) 
-u1))).(let H_x \def (csuba_gen_flat g c c2 t f H3) in (let H5 \def H_x in 
-(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) 
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g c d2))) (or (ex2 C (\lambda 
-(d2: C).(drop (S n) 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 (S n) 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 (x0: C).(\lambda (x1: 
-T).(\lambda (H6: (eq C c2 (CHead x0 (Flat f) x1))).(\lambda (H7: (csuba g c 
-x0)).(eq_ind_r C (CHead x0 (Flat f) x1) (\lambda (c0: C).(or (ex2 C (\lambda 
-(d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H8 \def (H0 d1 u1 H4 g 
-x0 H7) in (or_ind (ex2 C (\lambda (d2: C).(drop (S n) O x0 (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 (S n) O x0 (CHead d2 (Bind Abbr) 
+(u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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).(drop (S n) O (CHead x0 (Flat f) x1) 
+a)))))) (\lambda (H9: (ex2 C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 
+(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda 
+(d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba 
+g d1 d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) 
 (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 (S n) O (CHead x0 
 (Flat f) x1) (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 (H9: (ex2 C (\lambda 
-(d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba 
-g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind 
-Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: 
+(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x: C).(\lambda (H10: 
+(drop (S n) O x0 (CHead x (Bind Abst) u1))).(\lambda (H11: (csuba g d1 
+x)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) 
+(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 (S n) O (CHead x0 
+(Flat f) x1) (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).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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 (x: C).(\lambda (H10: (drop (S n) O x0 (CHead x (Bind Abst) 
-u1))).(\lambda (H11: (csuba g d1 x)).(or_introl (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u2))))) 
+(d2: C).(csuba g d1 d2)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abst) u1) 
+H10 x1) H11))))) H9)) (\lambda (H9: (ex4_3 C T A (\lambda (d2: C).(\lambda 
+(u2: T).(\lambda (_: A).(drop (S n) O x0 (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).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Flat f) n 
-x0 (CHead x (Bind Abst) u1) H10 x1) H11))))) H9)) (\lambda (H9: (ex4_3 C T A 
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O x0 (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 (_: 
+(\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 (S n) O x0 (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 
@@ -814,793 +803,1654 @@ Abbr) x3) H10 x1) H11 H12 H13))))))))) H9)) H8)) c2 H6))))) H5)))))) k H2
 theorem csuba_drop_abst_rev:
  \forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop i 
 O c1 (CHead d1 (Bind Abst) u)) \to (\forall (g: G).(\forall (c2: C).((csuba g 
-c2 c1) \to (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u))) 
-(\lambda (d2: C).(csuba g d2 d1))))))))))
+c2 c1) \to (or (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))))))))))))
 \def
  \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c1: C).(\forall (d1: 
 C).(\forall (u: T).((drop n O c1 (CHead d1 (Bind Abst) u)) \to (\forall (g: 
-G).(\forall (c2: C).((csuba g c2 c1) \to (ex2 C (\lambda (d2: C).(drop n O c2 
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))))))))))) 
-(\lambda (c1: C).(\lambda (d1: C).(\lambda (u: T).(\lambda (H: (drop O O c1 
-(CHead d1 (Bind Abst) u))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H0: 
-(csuba g c2 c1)).(let H1 \def (eq_ind C c1 (\lambda (c: C).(csuba g c2 c)) H0 
-(CHead d1 (Bind Abst) u) (drop_gen_refl c1 (CHead d1 (Bind Abst) u) H)) in 
-(let H_x \def (csuba_gen_abst_rev g d1 c2 u H1) in (let H2 \def H_x in 
-(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
-C).(csuba g d2 d1)) (ex2 C (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind 
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x: C).(\lambda (H3: 
-(eq C c2 (CHead x (Bind Abst) u))).(\lambda (H4: (csuba g x d1)).(eq_ind_r C 
-(CHead x (Bind Abst) u) (\lambda (c: C).(ex2 C (\lambda (d2: C).(drop O O c 
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))) (ex_intro2 C 
-(\lambda (d2: C).(drop O O (CHead x (Bind Abst) u) (CHead d2 (Bind Abst) u))) 
-(\lambda (d2: C).(csuba g d2 d1)) x (drop_refl (CHead x (Bind Abst) u)) H4) 
-c2 H3)))) H2))))))))))) (\lambda (n: nat).(\lambda (H: ((\forall (c1: 
-C).(\forall (d1: C).(\forall (u: T).((drop n O c1 (CHead d1 (Bind Abst) u)) 
-\to (\forall (g: G).(\forall (c2: C).((csuba g c2 c1) \to (ex2 C (\lambda 
-(d2: C).(drop n O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
-d1)))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1: 
+G).(\forall (c2: C).((csuba g c2 c1) \to (or (ex2 C (\lambda (d2: C).(drop n 
+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 n O c2 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))) (\lambda (c1: 
+C).(\lambda (d1: C).(\lambda (u: T).(\lambda (H: (drop O O c1 (CHead d1 (Bind 
+Abst) u))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H0: (csuba g c2 
+c1)).(let H1 \def (eq_ind C c1 (\lambda (c: C).(csuba g c2 c)) H0 (CHead d1 
+(Bind Abst) u) (drop_gen_refl c1 (CHead d1 (Bind Abst) u) H)) in (let H_x 
+\def (csuba_gen_abst_rev g d1 c2 u H1) in (let H2 \def H_x in (or_ind (ex2 C 
+(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba 
+g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or 
+(ex2 C (\lambda (d2: C).(drop O 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 O O 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (H3: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) 
+u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(eq C c2 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C 
+(\lambda (d2: C).(drop O 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 O O 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x: C).(\lambda (H4: (eq C c2 (CHead x (Bind Abst) 
+u))).(\lambda (H5: (csuba g x d1)).(eq_ind_r C (CHead x (Bind Abst) u) 
+(\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (CHead d2 (Bind Abst) 
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1)))))) (or_introl (ex2 C (\lambda (d2: C).(drop O O 
+(CHead x (Bind Abst) u) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g 
+d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x 
+(Bind Abst) u) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop O O (CHead x (Bind 
+Abst) u) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x 
+(drop_refl (CHead x (Bind Abst) u)) H5)) c2 H4)))) H3)) (\lambda (H3: (ex2_2 
+C T (\lambda (d2: C).(\lambda (u2: T).(eq C 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).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop O 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 O O c2 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H4: (eq C c2 (CHead x0 (Bind Void) 
+x1))).(\lambda (H5: (csuba g x0 d1)).(eq_ind_r C (CHead x0 (Bind Void) x1) 
+(\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (CHead d2 (Bind Abst) 
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1)))))) (or_intror (ex2 C (\lambda (d2: C).(drop O O 
+(CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba 
+g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x0 
+(Bind Void) x1) (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).(drop O O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_refl (CHead x0 (Bind 
+Void) x1)) H5)) c2 H4))))) H3)) H2))))))))))) (\lambda (n: nat).(\lambda (H: 
+((\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop n O c1 (CHead d1 
+(Bind Abst) u)) \to (\forall (g: G).(\forall (c2: C).((csuba g c2 c1) \to (or 
+(ex2 C (\lambda (d2: C).(drop n 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 n O 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1: 
 C).(\forall (u: T).((drop (S n) O c (CHead d1 (Bind Abst) u)) \to (\forall 
-(g: G).(\forall (c2: C).((csuba g c2 c) \to (ex2 C (\lambda (d2: C).(drop (S 
-n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))))))))) 
+(g: G).(\forall (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(drop 
+(S n) 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 (S n) O c2 (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))))) 
 (\lambda (n0: nat).(\lambda (d1: C).(\lambda (u: T).(\lambda (H0: (drop (S n) 
 O (CSort n0) (CHead d1 (Bind Abst) u))).(\lambda (g: G).(\lambda (c2: 
 C).(\lambda (_: (csuba g c2 (CSort n0))).(and3_ind (eq C (CHead d1 (Bind 
-Abst) u) (CSort n0)) (eq nat (S n) O) (eq nat O O) (ex2 C (\lambda (d2: 
+Abst) u) (CSort n0)) (eq nat (S n) O) (eq nat O O) (or (ex2 C (\lambda (d2: 
 C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
-d1))) (\lambda (H2: (eq C (CHead d1 (Bind Abst) u) (CSort n0))).(\lambda (_: 
-(eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (match H2 in eq 
-return (\lambda (c: C).(\lambda (_: (eq ? ? c)).((eq C c (CSort n0)) \to (ex2 
+d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) 
+(\lambda (_: (eq C (CHead d1 (Bind Abst) u) (CSort n0))).(\lambda (H3: (eq 
+nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S n) 
+(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O 
+\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2 
 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
-C).(csuba g d2 d1)))))) with [refl_equal \Rightarrow (\lambda (H5: (eq C 
-(CHead d1 (Bind Abst) u) (CSort n0))).(let H6 \def (eq_ind C (CHead d1 (Bind 
-Abst) u) (\lambda (e: C).(match e in C return (\lambda (_: C).Prop) with 
-[(CSort _) \Rightarrow False | (CHead _ _ _) \Rightarrow True])) I (CSort n0) 
-H5) in (False_ind (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind 
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) H6)))]) in (H5 (refl_equal C 
-(CSort n0))))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u) 
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) 
+O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d1))))) H5))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u) 
 H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u: 
 T).((drop (S n) O c (CHead d1 (Bind Abst) u)) \to (\forall (g: G).(\forall 
-(c2: C).((csuba g c2 c) \to (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead 
-d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))))))))))).(\lambda (k: 
-K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H1: (drop (S n) 
-O (CHead c k t) (CHead d1 (Bind Abst) u))).(\lambda (g: G).(\lambda (c2: 
-C).(\lambda (H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0: K).((csuba 
-g c2 (CHead c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abst) u)) \to 
-(ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda 
-(d2: C).(csuba g d2 d1)))))) (\lambda (b: B).(\lambda (H3: (csuba g c2 (CHead 
-c (Bind b) t))).(\lambda (H4: (drop (r (Bind b) n) O c (CHead d1 (Bind Abst) 
-u))).(B_ind (\lambda (b0: B).((csuba g c2 (CHead c (Bind b0) t)) \to ((drop 
-(r (Bind b0) n) O c (CHead d1 (Bind Abst) u)) \to (ex2 C (\lambda (d2: 
+(c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))).(\lambda 
+(k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H1: (drop 
+(S n) O (CHead c k t) (CHead d1 (Bind Abst) u))).(\lambda (g: G).(\lambda 
+(c2: C).(\lambda (H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0: 
+K).((csuba g c2 (CHead c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abst) 
+u)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (b: B).(\lambda (H3: 
+(csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop (r (Bind b) n) O c 
+(CHead d1 (Bind Abst) u))).(B_ind (\lambda (b0: B).((csuba g c2 (CHead c 
+(Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead d1 (Bind Abst) u)) \to 
+(or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1)))))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr) 
+t))).(\lambda (H6: (drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abst) 
+u))).(let H_x \def (csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in 
+(or3_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda 
+(d2: C).(csuba g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: 
+T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\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 c t a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 c)))) (or (ex2 C (\lambda (d2: 
 C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
-d1)))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr) t))).(\lambda (H6: 
-(drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abst) u))).(let H_x \def 
-(csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in (or_ind (ex2 C 
-(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba 
-g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq 
-C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda 
-(_: A).(csuba g d2 c)))) (\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 c t a))))) (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (H8: (ex2 C 
-(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba 
-g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) 
-(\lambda (d2: C).(csuba g d2 c)) (ex2 C (\lambda (d2: C).(drop (S n) O c2 
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x: 
-C).(\lambda (H9: (eq C c2 (CHead x (Bind Abbr) t))).(\lambda (H10: (csuba g x 
-c)).(eq_ind_r C (CHead x (Bind Abbr) t) (\lambda (c0: C).(ex2 C (\lambda (d2: 
-C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
-d1)))) (let H11 \def (H c d1 u H6 g x H10) in (ex2_ind C (\lambda (d2: 
+d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) 
+(\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) 
+(\lambda (d2: C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 
+(CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba g d2 c)) (or (ex2 C 
+(\lambda (d2: C).(drop (S n) 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 (S n) 
+O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq C c2 (CHead x (Bind Abbr) 
+t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C (CHead x (Bind Abbr) t) 
+(\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind 
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H11 \def (H c d1 u H6 g x 
+H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) 
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x 
+(Bind Abbr) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind 
+Abbr) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba 
+g d2 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: 
 C).(drop n O x (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) 
-(ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind 
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x0: C).(\lambda (H12: 
-(drop n O x (CHead x0 (Bind Abst) u))).(\lambda (H13: (csuba g x0 d1)).(let 
-H14 \def (refl_equal nat (r (Bind Abst) n)) in (let H15 \def (eq_ind nat n 
-(\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abst) u))) H12 (r (Bind Abst) 
-n) H14) in (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) 
+(or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x0: C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abst) u))).(\lambda (H14: 
+(csuba g x0 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x 
+(Bind Abbr) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind 
+Abbr) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba 
+g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) 
 t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop 
-(Bind Abbr) n x (CHead x0 (Bind Abst) u) H15 t) H13)))))) H11)) c2 H9)))) 
-H8)) (\lambda (H8: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda 
-(_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: 
-T).(\lambda (_: A).(csuba g d2 c)))) (\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 c t a)))))).(ex4_3_ind C T A (\lambda (d2: 
-C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) 
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\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 c t a)))) (ex2 C 
-(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
-C).(csuba g d2 d1))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: 
+(Bind Abbr) n x (CHead x0 (Bind Abst) u) H13 t) H14))))) H12)) (\lambda (H12: 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (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 n O x (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda 
+(d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead x0 (Bind Void) 
+x1))).(\lambda (H14: (csuba g x0 d1)).(or_intror (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u))) (\lambda 
+(d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop 
+(S n) O (CHead x (Bind Abbr) t) (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).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 
+(drop_drop (Bind Abbr) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12)) 
+H11)) c2 H9)))) H8)) (\lambda (H8: (ex4_3 C T A (\lambda (d2: C).(\lambda 
+(u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\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 c t a)))))).(ex4_3_ind C T A 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind 
+Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 
+c)))) (\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 c t a)))) 
+(or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: 
 A).(\lambda (H9: (eq C c2 (CHead x0 (Bind Abst) x1))).(\lambda (H10: (csuba g 
 x0 c)).(\lambda (_: (arity g x0 x1 (asucc g x2))).(\lambda (_: (arity g c t 
-x2)).(eq_ind_r C (CHead x0 (Bind Abst) x1) (\lambda (c0: C).(ex2 C (\lambda 
-(d2: C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g 
-d2 d1)))) (let H13 \def (H c d1 u H6 g x0 H10) in (ex2_ind C (\lambda (d2: 
-C).(drop n O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) 
+x2)).(eq_ind_r C (CHead x0 (Bind Abst) x1) (\lambda (c0: C).(or (ex2 C 
+(\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) 
+O c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d1)))))) (let H13 \def (H c d1 u H6 g x0 H10) in (or_ind (ex2 C (\lambda 
+(d2: C).(drop n O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
+d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or 
 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x: C).(\lambda 
-(H14: (drop n O x0 (CHead x (Bind Abst) u))).(\lambda (H15: (csuba g x 
-d1)).(let H16 \def (refl_equal nat (r (Bind Abst) n)) in (let H17 \def 
-(eq_ind nat n (\lambda (n0: nat).(drop n0 O x0 (CHead x (Bind Abst) u))) H14 
-(r (Bind Abst) n) H16) in (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead 
-x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
-d1)) x (drop_drop (Bind Abst) n x0 (CHead x (Bind Abst) u) H17 x1) H15)))))) 
-H13)) c2 H9)))))))) H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind 
-Abst) t))).(\lambda (H6: (drop (r (Bind Abst) n) O c (CHead d1 (Bind Abst) 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(H14: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x0 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind 
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x: C).(\lambda (H15: (drop n O x0 (CHead x (Bind Abst) u))).(\lambda (H16: 
+(csuba g x d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
+(Bind Abst) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind 
+Abst) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
+(Bind Abst) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) 
+x (drop_drop (Bind Abst) n x0 (CHead x (Bind Abst) u) H15 x1) H16))))) H14)) 
+(\lambda (H14: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 
+(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 n O x0 (CHead 
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or 
+(ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x3: C).(\lambda (x4: T).(\lambda (H15: (drop n O x0 (CHead x3 (Bind Void) 
+x4))).(\lambda (H16: (csuba g x3 d1)).(or_intror (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Abst) x1) (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).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x3 x4 
+(drop_drop (Bind Abst) n x0 (CHead x3 (Bind Void) x4) H15 x1) H16)))))) H14)) 
+H13)) c2 H9)))))))) H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+c))) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H9: 
+(eq C c2 (CHead x0 (Bind Void) x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r 
+C (CHead x0 (Bind Void) x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: 
+C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
+d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let 
+H11 \def (H c d1 u H6 g x0 H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O 
+x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H12: (ex2 C 
+(\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x0 (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda 
+(H13: (drop n O x0 (CHead x (Bind Abst) u))).(\lambda (H14: (csuba g x 
+d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) 
+x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop 
+(Bind Void) n x0 (CHead x (Bind Abst) u) H13 x1) H14))))) H12)) (\lambda 
+(H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (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 n O x0 (CHead 
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or 
+(ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void) 
+x3))).(\lambda (H14: (csuba g x2 d1)).(or_intror (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Void) x1) (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).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 
+(drop_drop (Bind Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12)) 
+H11)) c2 H9))))) H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abst) 
+t))).(\lambda (H6: (drop (r (Bind Abst) n) O c (CHead d1 (Bind Abst) 
 u))).(let H_x \def (csuba_gen_abst_rev g c c2 t H5) in (let H7 \def H_x in 
-(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: 
-C).(csuba g d2 c)) (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind 
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x: C).(\lambda (H8: 
-(eq C c2 (CHead x (Bind Abst) t))).(\lambda (H9: (csuba g x c)).(eq_ind_r C 
-(CHead x (Bind Abst) t) (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) 
-O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))) (let H10 
-\def (H c d1 u H6 g x H9) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead 
-d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (ex2 C (\lambda (d2: 
-C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda 
-(d2: C).(csuba g d2 d1))) (\lambda (x0: C).(\lambda (H11: (drop n O x (CHead 
-x0 (Bind Abst) u))).(\lambda (H12: (csuba g x0 d1)).(let H13 \def (refl_equal 
-nat (r (Bind Abst) n)) in (let H14 \def (eq_ind nat n (\lambda (n0: 
-nat).(drop n0 O x (CHead x0 (Bind Abst) u))) H11 (r (Bind Abst) n) H13) in 
-(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop (Bind Abst) 
-n x (CHead x0 (Bind Abst) u) H14 t) H12)))))) H10)) c2 H8)))) H7))))) 
-(\lambda (H5: (csuba g c2 (CHead c (Bind Void) t))).(\lambda (H6: (drop (r 
-(Bind Void) n) O c (CHead d1 (Bind Abst) u))).(let H_x \def 
-(csuba_gen_void_rev g c c2 t H5) in (let H7 \def H_x in (ex2_ind C (\lambda 
-(d2: C).(eq C c2 (CHead d2 (Bind Void) t))) (\lambda (d2: C).(csuba g d2 c)) 
-(ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda 
-(d2: C).(csuba g d2 d1))) (\lambda (x: C).(\lambda (H8: (eq C c2 (CHead x 
-(Bind Void) t))).(\lambda (H9: (csuba g x c)).(eq_ind_r C (CHead x (Bind 
-Void) t) (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))) (let H10 \def (H c d1 u 
-H6 g x H9) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) 
-u))) (\lambda (d2: C).(csuba g d2 d1)) (ex2 C (\lambda (d2: C).(drop (S n) O 
-(CHead x (Bind Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g 
-d2 d1))) (\lambda (x0: C).(\lambda (H11: (drop n O x (CHead x0 (Bind Abst) 
-u))).(\lambda (H12: (csuba g x0 d1)).(let H13 \def (refl_equal nat (r (Bind 
-Abst) n)) in (let H14 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x 
-(CHead x0 (Bind Abst) u))) H11 (r (Bind Abst) n) H13) in (ex_intro2 C 
+(or_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda 
+(d2: C).(csuba g d2 c))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+c)))) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1))))) (\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2 
+(CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g d2 c)))).(ex2_ind C 
+(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba 
+g d2 c)) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq C c2 
+(CHead x (Bind Abst) t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C (CHead x 
+(Bind Abst) t) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H11 \def (H 
+c d1 u H6 g x H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n) 
+O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba 
+g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead 
+x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C 
+(\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind 
+Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 
+C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x0: C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abst) 
+u))).(\lambda (H14: (csuba g x0 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop 
+(S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) 
+O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S 
+n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)) x0 (drop_drop (Bind Abst) n x (CHead x0 (Bind Abst) u) 
+H13 t) H14))))) H12)) (\lambda (H12: (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop n O x (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 n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind 
+Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 
+C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead 
+x0 (Bind Void) x1))).(\lambda (H14: (csuba g x0 d1)).(or_intror (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) 
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop (S n) O (CHead x (Bind Abst) t) (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).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 
+(drop_drop (Bind Abst) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12)) 
+H11)) c2 H9)))) H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+c))) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H9: 
+(eq C c2 (CHead x0 (Bind Void) x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r 
+C (CHead x0 (Bind Void) x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: 
+C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 
+d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let 
+H11 \def (H c d1 u H6 g x0 H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O 
+x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H12: (ex2 C 
+(\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x0 (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda 
+(H13: (drop n O x0 (CHead x (Bind Abst) u))).(\lambda (H14: (csuba g x 
+d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) 
+x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop 
+(Bind Void) n x0 (CHead x (Bind Abst) u) H13 x1) H14))))) H12)) (\lambda 
+(H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (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 n O x0 (CHead 
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or 
+(ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void) 
+x3))).(\lambda (H14: (csuba g x2 d1)).(or_intror (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) 
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Void) x1) (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).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 
+(drop_drop (Bind Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12)) 
+H11)) c2 H9))))) H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Void) 
+t))).(\lambda (H6: (drop (r (Bind Void) n) O c (CHead d1 (Bind Abst) 
+u))).(let H_x \def (csuba_gen_void_rev g c c2 t H5) in (let H7 \def H_x in 
+(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Void) t))) (\lambda (d2: 
+C).(csuba g d2 c)) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H8: (eq 
+C c2 (CHead x (Bind Void) t))).(\lambda (H9: (csuba g x c)).(eq_ind_r C 
+(CHead x (Bind Void) t) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S 
+n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 
+C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H10 \def (H 
+c d1 u H6 g x H9) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n) 
+O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba 
+g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead 
+x (Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (H11: (ex2 C (\lambda (d2: C).(drop n O x 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C 
+(\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind 
+Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 
+C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Void) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0 (Bind Abst) 
+u))).(\lambda (H13: (csuba g x0 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop 
+(S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) 
+O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S 
+n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)) x0 (drop_drop (Bind Void) n x (CHead x0 (Bind Abst) u) 
+H12 t) H13))))) H11)) (\lambda (H11: (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop n O x (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 n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind 
+Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 
+C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Void) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H12: (drop n O x (CHead 
+x0 (Bind Void) x1))).(\lambda (H13: (csuba g x0 d1)).(or_intror (ex2 C 
 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) 
-u))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop (Bind Void) n x (CHead 
-x0 (Bind Abst) u) H14 t) H12)))))) H10)) c2 H8)))) H7))))) b H3 H4)))) 
-(\lambda (f: F).(\lambda (H3: (csuba g c2 (CHead c (Flat f) t))).(\lambda 
-(H4: (drop (r (Flat f) n) O c (CHead d1 (Bind Abst) u))).(let H_x \def 
-(csuba_gen_flat_rev g c c2 t f H3) in (let H5 \def H_x in (ex2_2_ind C T 
-(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda 
-(d2: C).(\lambda (_: T).(csuba g d2 c))) (ex2 C (\lambda (d2: C).(drop (S n) 
-O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda 
-(x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0 (Flat f) 
-x1))).(\lambda (H7: (csuba g x0 c)).(eq_ind_r C (CHead x0 (Flat f) x1) 
-(\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind 
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))) (let H8 \def (H0 d1 u H4 g x0 
-H7) in (ex2_ind C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst) 
-u))) (\lambda (d2: C).(csuba g d2 d1)) (ex2 C (\lambda (d2: C).(drop (S n) O 
-(CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g 
-d2 d1))) (\lambda (x: C).(\lambda (H9: (drop (S n) O x0 (CHead x (Bind Abst) 
-u))).(\lambda (H10: (csuba g x d1)).(ex_intro2 C (\lambda (d2: C).(drop (S n) 
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop (S n) O (CHead x (Bind Void) t) (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).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 
+(drop_drop (Bind Void) n x (CHead x0 (Bind Void) x1) H12 t) H13)))))) H11)) 
+H10)) c2 H8)))) H7))))) b H3 H4)))) (\lambda (f: F).(\lambda (H3: (csuba g c2 
+(CHead c (Flat f) t))).(\lambda (H4: (drop (r (Flat f) n) O c (CHead d1 (Bind 
+Abst) u))).(let H_x \def (csuba_gen_flat_rev g c c2 t f H3) in (let H5 \def 
+H_x in (ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 
+(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c))) (or (ex2 C 
+(\lambda (d2: C).(drop (S n) 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 (S n) 
+O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0 
+(Flat f) x1))).(\lambda (H7: (csuba g x0 c)).(eq_ind_r C (CHead x0 (Flat f) 
+x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H8 \def (H0 d1 u H4 g x0 
+H7) in (or_ind (ex2 C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst) 
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n) 
 O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g 
-d2 d1)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abst) u) H9 x1) H10)))) 
+d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 
+(Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (H9: (ex2 C (\lambda (d2: C).(drop (S n) O x0 
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C 
+(\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat 
+f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C 
+T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x: C).(\lambda (H10: (drop (S n) O x0 (CHead x (Bind Abst) 
+u))).(\lambda (H11: (csuba g x d1)).(or_introl (ex2 C (\lambda (d2: C).(drop 
+(S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) 
+O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S 
+n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d1)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abst) u) H10 
+x1) H11))))) H9)) (\lambda (H9: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O x0 (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 (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
+(Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f) 
+x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (H10: (drop (S n) O x0 
+(CHead x2 (Bind Void) x3))).(\lambda (H11: (csuba g x2 d1)).(or_intror (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) 
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda 
+(u2: T).(drop (S n) O (CHead x0 (Flat f) x1) (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).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 
+(drop_drop (Flat f) n x0 (CHead x2 (Bind Void) x3) H10 x1) H11)))))) H9)) 
 H8)) c2 H6))))) H5)))))) k H2 (drop_gen_drop k c (CHead d1 (Bind Abst) u) t n 
 H1)))))))))))) c1)))) i).
 
 theorem csuba_drop_abbr_rev:
  \forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).((drop i 
 O c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba 
-g c2 c1) \to (or (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) 
+g c2 c1) \to (or3 (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)))))))))))))
+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))))))))))))
 \def
  \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c1: C).(\forall (d1: 
 C).(\forall (u1: T).((drop n O c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (g: 
-G).(\forall (c2: C).((csuba g c2 c1) \to (or (ex2 C (\lambda (d2: C).(drop n 
+G).(\forall (c2: C).((csuba g c2 c1) \to (or3 (ex2 C (\lambda (d2: C).(drop n 
 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 n 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)))))))))))))) (\lambda (c1: C).(\lambda (d1: C).(\lambda (u1: 
-T).(\lambda (H: (drop O O c1 (CHead d1 (Bind Abbr) u1))).(\lambda (g: 
-G).(\lambda (c2: C).(\lambda (H0: (csuba g c2 c1)).(let H1 \def (eq_ind C c1 
-(\lambda (c: C).(csuba g c2 c)) H0 (CHead d1 (Bind Abbr) u1) (drop_gen_refl 
-c1 (CHead d1 (Bind Abbr) u1) H)) in (let H_x \def (csuba_gen_abbr_rev g d1 c2 
-u1 H1) in (let H2 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C 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).(eq C c2 (CHead d2 (Bind Abst) 
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O c2 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))))))))))) (\lambda (c1: C).(\lambda (d1: C).(\lambda (u1: T).(\lambda 
+(H: (drop O O c1 (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda (c2: 
+C).(\lambda (H0: (csuba g c2 c1)).(let H1 \def (eq_ind C c1 (\lambda (c: 
+C).(csuba g c2 c)) H0 (CHead d1 (Bind Abbr) u1) (drop_gen_refl c1 (CHead d1 
+(Bind Abbr) u1) H)) in (let H_x \def (csuba_gen_abbr_rev g d1 c2 u1 H1) in 
+(let H2 \def H_x in (or3_ind (ex2 C (\lambda (d2: C).(eq C 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).(eq C 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).(eq C c2 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: 
+C).(drop O 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 O 
+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 O O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (H3: (ex2 C (\lambda (d2: C).(eq C c2 (CHead 
+d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda 
+(d2: C).(eq C c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 
+d1)) (or3 (ex2 C (\lambda (d2: C).(drop O 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 O 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 O O c2 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda 
+(H4: (eq C c2 (CHead x (Bind Abbr) u1))).(\lambda (H5: (csuba g x 
+d1)).(eq_ind_r C (CHead x (Bind Abbr) u1) (\lambda (c: C).(or3 (ex2 C 
+(\lambda (d2: C).(drop O O c (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 O O c (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 O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))))) (or3_intro0 (ex2 C (\lambda (d2: 
+C).(drop O O (CHead x (Bind Abbr) u1) (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 O O (CHead x (Bind Abbr) u1) (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))))) 
-(or (ex2 C (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abbr) u1))) (\lambda 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x (Bind Abbr) 
+u1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex_intro2 C (\lambda (d2: C).(drop O O (CHead x (Bind Abbr) u1) 
+(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_refl 
+(CHead x (Bind Abbr) u1)) H5)) c2 H4)))) H3)) (\lambda (H3: (ex4_3 C T A 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C 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)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(eq C 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)))) (or3 (ex2 C (\lambda (d2: 
+C).(drop O 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 O 
+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 O O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: 
+A).(\lambda (H4: (eq C c2 (CHead x0 (Bind Abst) x1))).(\lambda (H5: (csuba g 
+x0 d1)).(\lambda (H6: (arity g x0 x1 (asucc g x2))).(\lambda (H7: (arity g d1 
+u1 x2)).(eq_ind_r C (CHead x0 (Bind Abst) x1) (\lambda (c: C).(or3 (ex2 C 
+(\lambda (d2: C).(drop O O c (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 O O c (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 O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))))) (or3_intro1 (ex2 C (\lambda (d2: 
+C).(drop O O (CHead x0 (Bind Abst) x1) (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 O O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: 
+T).(\lambda (_: A).(drop O O (CHead x0 (Bind Abst) x1) (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 O O (CHead x0 (Bind Abst) 
+x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop O O (CHead x0 (Bind Abst) x1) (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)))))) (\lambda (H3: 
-(ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
-C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind 
-Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x0 x1 x2 
+(drop_refl (CHead x0 (Bind Abst) x1)) H5 H6 H7)) c2 H4)))))))) H3)) (\lambda 
+(H3: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C 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).(eq C c2 (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C (\lambda (d2: 
 C).(drop O 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 O 
 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)))))) (\lambda (x: C).(\lambda (H4: (eq C c2 (CHead x 
-(Bind Abbr) u1))).(\lambda (H5: (csuba g x d1)).(eq_ind_r C (CHead x (Bind 
-Abbr) u1) (\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (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 O O c (CHead d2 (Bind Abst) 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop O O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H4: (eq C 
+c2 (CHead x0 (Bind Void) x1))).(\lambda (H5: (csuba g x0 d1)).(eq_ind_r C 
+(CHead x0 (Bind Void) x1) (\lambda (c: C).(or3 (ex2 C (\lambda (d2: C).(drop 
+O O c (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 O O c (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 O O c (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) 
+(or3_intro2 (ex2 C (\lambda (d2: C).(drop O O (CHead x0 (Bind Void) x1) 
+(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 O O (CHead x0 (Bind 
+Void) x1) (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 O O (CHead x0 (Bind Void) x1) (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).(drop O O (CHead x0 (Bind Void) x1) (CHead 
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 
+x1 (drop_refl (CHead x0 (Bind Void) x1)) H5)) c2 H4))))) H3)) H2))))))))))) 
+(\lambda (n: nat).(\lambda (H: ((\forall (c1: C).(\forall (d1: C).(\forall 
+(u1: T).((drop n O c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (g: G).(\forall 
+(c2: C).((csuba g c2 c1) \to (or3 (ex2 C (\lambda (d2: C).(drop n 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 n 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))))))) (or_introl (ex2 C (\lambda (d2: C).(drop O O (CHead x (Bind Abbr) 
-u1) (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 O O (CHead x (Bind 
-Abbr) u1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: 
+a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O c2 (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1: 
+C).(\forall (u1: T).((drop (S n) O c (CHead d1 (Bind Abbr) u1)) \to (\forall 
+(g: G).(\forall (c2: C).((csuba g c2 c) \to (or3 (ex2 C (\lambda (d2: 
+C).(drop (S n) 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 (S 
+n) 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))))) (ex_intro2 C (\lambda (d2: 
-C).(drop O O (CHead x (Bind Abbr) u1) (CHead d2 (Bind Abbr) u1))) (\lambda 
-(d2: C).(csuba g d2 d1)) x (drop_refl (CHead x (Bind Abbr) u1)) H5)) c2 
-H4)))) H3)) (\lambda (H3: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: 
-T).(\lambda (_: A).(eq C 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)))))).(ex4_3_ind C T 
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind 
+(_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))))) (\lambda (n0: 
+nat).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H0: (drop (S n) O (CSort n0) 
+(CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (_: 
+(csuba g c2 (CSort n0))).(and3_ind (eq C (CHead d1 (Bind Abbr) u1) (CSort 
+n0)) (eq nat (S n) O) (eq nat O O) (or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1))))) (\lambda (_: (eq C (CHead d1 (Bind Abbr) u1) 
+(CSort n0))).(\lambda (H3: (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let 
+H5 \def (eq_ind nat (S n) (\lambda (ee: nat).(match ee in nat return (\lambda 
+(_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow True])) I O H3) 
+in (False_ind (or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) H5))))) 
+(drop_gen_sort n0 (S n) O (CHead d1 (Bind Abbr) u1) H0))))))))) (\lambda (c: 
+C).(\lambda (H0: ((\forall (d1: C).(\forall (u1: T).((drop (S n) O c (CHead 
+d1 (Bind Abbr) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c2 c) \to 
+(or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))).(\lambda 
+(k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H1: (drop 
+(S n) O (CHead c k t) (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda 
+(c2: C).(\lambda (H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0: 
+K).((csuba g c2 (CHead c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abbr) 
+u1)) \to (or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda 
+(b: B).(\lambda (H3: (csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop 
+(r (Bind b) n) O c (CHead d1 (Bind Abbr) u1))).(B_ind (\lambda (b0: 
+B).((csuba g c2 (CHead c (Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead 
+d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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)))) (or (ex2 C (\lambda (d2: C).(drop O 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 O 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)))))) (\lambda (x0: 
-C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H4: (eq C c2 (CHead x0 (Bind 
-Abst) x1))).(\lambda (H5: (csuba g x0 d1)).(\lambda (H6: (arity g x0 x1 
-(asucc g x2))).(\lambda (H7: (arity g d1 u1 x2)).(eq_ind_r C (CHead x0 (Bind 
-Abst) x1) (\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (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 O O c (CHead d2 (Bind Abst) 
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr) t))).(\lambda (H6: 
+(drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def 
+(csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in (or3_ind (ex2 C 
+(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba 
+g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq 
+C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda 
+(_: A).(csuba g d2 c)))) (\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 c t a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+c)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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))))))) (or_intror (ex2 C (\lambda (d2: C).(drop O O (CHead x0 (Bind Abst) 
-x1) (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 O O (CHead x0 (Bind 
-Abst) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: 
+a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda 
+(d2: C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 
+(Bind Abbr) t))) (\lambda (d2: C).(csuba g d2 c)) (or3 (ex2 C (\lambda (d2: 
+C).(drop (S n) 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 (S 
+n) 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))))) (ex4_3_intro C T A (\lambda (d2: 
-C).(\lambda (u2: T).(\lambda (_: A).(drop O O (CHead x0 (Bind Abst) x1) 
-(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: 
-A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: 
+(_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq 
+C c2 (CHead x (Bind Abbr) t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C 
+(CHead x (Bind Abbr) t) (\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop 
+(S n) O c0 (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 (S n) O 
+c0 (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)))) x0 x1 x2 (drop_refl (CHead x0 (Bind Abst) x1)) H5 
-H6 H7)) c2 H4)))))))) H3)) H2))))))))))) (\lambda (n: nat).(\lambda (H: 
-((\forall (c1: C).(\forall (d1: C).(\forall (u1: T).((drop n O c1 (CHead d1 
-(Bind Abbr) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c2 c1) \to 
-(or (ex2 C (\lambda (d2: C).(drop n 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 n O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1)))))) (let H11 \def (H c d1 u1 H6 g x H10) in (or3_ind 
+(ex2 C (\lambda (d2: C).(drop n O x (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 n O x (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 n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S 
+n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: 
+C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) 
+(or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) 
+t) (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 (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abbr) u1))).(\lambda (H14: 
+(csuba g x0 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x 
+(Bind Abbr) t) (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 (S n) O 
+(CHead x (Bind Abbr) t) (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))))))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1: 
-C).(\forall (u1: T).((drop (S n) O c (CHead d1 (Bind Abbr) u1)) \to (\forall 
-(g: G).(\forall (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(drop 
-(S n) 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 (S n) O 
-c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abbr) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) 
+(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop 
+(Bind Abbr) n x (CHead x0 (Bind Abbr) u1) H13 t) H14))))) H12)) (\lambda 
+(H12: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n 
+O x (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))))))))))))) (\lambda (n0: nat).(\lambda (d1: 
-C).(\lambda (u1: T).(\lambda (H0: (drop (S n) O (CSort n0) (CHead d1 (Bind 
-Abbr) u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (_: (csuba g c2 (CSort 
-n0))).(and3_ind (eq C (CHead d1 (Bind Abbr) u1) (CSort n0)) (eq nat (S n) O) 
-(eq nat O O) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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)))))) 
-(\lambda (H2: (eq C (CHead d1 (Bind Abbr) u1) (CSort n0))).(\lambda (_: (eq 
-nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (match H2 in eq return 
-(\lambda (c: C).(\lambda (_: (eq ? ? c)).((eq C c (CSort n0)) \to (or (ex2 C 
-(\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+(a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: 
+T).(\lambda (_: A).(drop n O x (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))))))))) with 
-[refl_equal \Rightarrow (\lambda (H5: (eq C (CHead d1 (Bind Abbr) u1) (CSort 
-n0))).(let H6 \def (eq_ind C (CHead d1 (Bind Abbr) u1) (\lambda (e: C).(match 
-e in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | 
-(CHead _ _ _) \Rightarrow True])) I (CSort n0) H5) in (False_ind (or (ex2 C 
-(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) 
+(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 (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H13: (drop n O x (CHead x0 
+(Bind Abst) x1))).(\lambda (H14: (csuba g x0 d1)).(\lambda (H15: (arity g x0 
+x1 (asucc g x2))).(\lambda (H16: (arity g d1 u1 x2)).(or3_intro1 (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) 
+(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 (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x 
+(Bind Abbr) t) (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)))) x0 x1 x2 (drop_drop (Bind Abbr) n 
+x (CHead x0 (Bind Abst) x1) H13 t) H14 H15 H16))))))))) H12)) (\lambda (H12: 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (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 n O x (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) 
+(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 (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead x0 (Bind Void) 
+x1))).(\lambda (H14: (csuba g x0 d1)).(or3_intro2 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x 
+(Bind Abbr) t) (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).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_drop (Bind 
+Abbr) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12)) H11)) c2 H9)))) 
+H8)) (\lambda (H8: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda 
+(_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: 
+T).(\lambda (_: A).(csuba g d2 c)))) (\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 c t a)))))).(ex4_3_ind C T A (\lambda (d2: 
+C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) 
+(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\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 c t a)))) (or3 (ex2 
+C (\lambda (d2: C).(drop (S n) 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 (S n) 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)))))) H6)))]) in (H5 
-(refl_equal C (CSort n0))))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind 
-Abbr) u1) H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: 
-C).(\forall (u1: T).((drop (S n) O c (CHead d1 (Bind Abbr) u1)) \to (\forall 
-(g: G).(\forall (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(drop 
-(S n) 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 (S n) O 
-c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H9: (eq C c2 (CHead x0 (Bind 
+Abst) x1))).(\lambda (H10: (csuba g x0 c)).(\lambda (_: (arity g x0 x1 (asucc 
+g x2))).(\lambda (_: (arity g c t x2)).(eq_ind_r C (CHead x0 (Bind Abst) x1) 
+(\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop (S n) O c0 (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 (S n) O c0 (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 (S n) O c0 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))))) (let H13 \def (H c d1 u1 H6 g x0 H10) in (or3_ind (ex2 C (\lambda 
+(d2: C).(drop n O x0 (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 n 
+O x0 (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)))))))))))))).(\lambda (k: K).(\lambda (t: 
-T).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H1: (drop (S n) O (CHead c k 
-t) (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H2: 
-(csuba g c2 (CHead c k t))).(K_ind (\lambda (k0: K).((csuba g c2 (CHead c k0 
-t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abbr) u1)) \to (or (ex2 C 
-(\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
+(Bind Abst) x1) (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 (S 
+n) O (CHead x0 (Bind Abst) x1) (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))))))))) (\lambda (b: 
-B).(\lambda (H3: (csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop (r 
-(Bind b) n) O c (CHead d1 (Bind Abbr) u1))).(B_ind (\lambda (b0: B).((csuba g 
-c2 (CHead c (Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead d1 (Bind 
-Abbr) u1)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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))))))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr) t))).(\lambda (H6: 
-(drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def 
-(csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in (or_ind (ex2 C 
-(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba 
-g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq 
-C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda 
-(_: A).(csuba g d2 c)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (H14: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: 
+C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) 
+(or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (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 (S n) O (CHead x0 (Bind Abst) 
+x1) (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 c t a))))) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda 
+(H15: (drop n O x0 (CHead x (Bind Abbr) u1))).(\lambda (H16: (csuba g x 
+d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) 
+x1) (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 (S n) O (CHead x0 
+(Bind Abst) x1) (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 (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Bind Abst) n x0 
+(CHead x (Bind Abbr) u1) H15 x1) H16))))) H14)) (\lambda (H14: (ex4_3 C T A 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 (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)))))) (\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind 
-Abbr) t))) (\lambda (d2: C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq 
-C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba g d2 c)) (or (ex2 C 
-(\lambda (d2: C).(drop (S n) 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 (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop n O x0 (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)))) (or3 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Abst) x1) (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 (S n) O (CHead x0 (Bind Abst) x1) (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 (S n) O (CHead 
+x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: 
+A).(\lambda (H15: (drop n O x0 (CHead x3 (Bind Abst) x4))).(\lambda (H16: 
+(csuba g x3 d1)).(\lambda (H17: (arity g x3 x4 (asucc g x5))).(\lambda (H18: 
+(arity g d1 u1 x5)).(or3_intro1 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead 
+x0 (Bind Abst) x1) (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 (S 
+n) O (CHead x0 (Bind Abst) x1) (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)))))) (\lambda (x: 
-C).(\lambda (H9: (eq C c2 (CHead x (Bind Abbr) t))).(\lambda (H10: (csuba g x 
-c)).(eq_ind_r C (CHead x (Bind Abbr) t) (\lambda (c0: C).(or (ex2 C (\lambda 
-(d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H11 \def (H c d1 u1 H6 g 
-x H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (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 n O x (CHead d2 (Bind Abst) u2))))) 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop (S n) O (CHead x0 (Bind Abst) x1) (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))))) (or 
-(ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) 
-(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 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x3 x4 x5 
+(drop_drop (Bind Abst) n x0 (CHead x3 (Bind Abst) x4) H15 x1) H16 H17 
+H18))))))))) H14)) (\lambda (H14: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop n O x0 (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 
+n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) 
+(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 (S n) O (CHead x0 
+(Bind Abst) x1) (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 (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x3: C).(\lambda (x4: T).(\lambda (H15: (drop n O x0 (CHead x3 (Bind Void) 
+x4))).(\lambda (H16: (csuba g x3 d1)).(or3_intro2 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Abst) x1) (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 (S n) O (CHead x0 (Bind Abst) x1) (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 (S n) O (CHead 
+x0 (Bind Abst) x1) (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).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x3 x4 (drop_drop (Bind 
+Abst) n x0 (CHead x3 (Bind Void) x4) H15 x1) H16)))))) H14)) H13)) c2 
+H9)))))))) H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C 
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+c))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x0: C).(\lambda (x1: T).(\lambda (H9: (eq C c2 (CHead x0 (Bind Void) 
+x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r C (CHead x0 (Bind Void) x1) 
+(\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop (S n) O c0 (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 (S n) O c0 (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 (S n) O c0 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))))) (let H11 \def (H c d1 u1 H6 g x0 H10) in (or3_ind (ex2 C (\lambda 
+(d2: C).(drop n O x0 (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 n 
+O x0 (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)))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n 
-O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind 
-C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
-C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind 
-Abbr) t) (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 (S n) O 
-(CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
+(Bind Void) x1) (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 (S 
+n) O (CHead x0 (Bind Void) x1) (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)))))) (\lambda (x0: 
-C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abbr) u1))).(\lambda (H14: 
-(csuba g x0 d1)).(let H15 \def (refl_equal nat (r (Bind Abst) n)) in (let H16 
-\def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abbr) 
-u1))) H13 (r (Bind Abst) n) H15) in (or_introl (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) (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))))) 
-(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop (Bind Abbr) 
-n x (CHead x0 (Bind Abbr) u1) H16 t) H14))))))) H12)) (\lambda (H12: (ex4_3 C 
-T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (CHead d2 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: 
+C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) 
+(or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) 
+x1) (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 (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda 
+(H13: (drop n O x0 (CHead x (Bind Abbr) u1))).(\lambda (H14: (csuba g x 
+d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) 
+x1) (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 (S n) O (CHead x0 
+(Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Bind Void) n x0 
+(CHead x (Bind Abbr) u1) H13 x1) H14))))) H12)) (\lambda (H12: (ex4_3 C T A 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 (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)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
-A).(drop n O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: 
+A).(drop n O x0 (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)))) (or (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x (Bind Abbr) t) (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 (S n) O (CHead x (Bind Abbr) t) (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)))))) 
-(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H13: (drop n O x 
-(CHead x0 (Bind Abst) x1))).(\lambda (H14: (csuba g x0 d1)).(\lambda (H15: 
-(arity g x0 x1 (asucc g x2))).(\lambda (H16: (arity g d1 u1 x2)).(let H17 
-\def (refl_equal nat (r (Bind Abst) n)) in (let H18 \def (eq_ind nat n 
-(\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abst) x1))) H13 (r (Bind 
-Abst) n) H17) in (or_intror (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x 
-(Bind Abbr) t) (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 (S n) O 
-(CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+(_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead 
+x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: 
+A).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Abst) x3))).(\lambda (H14: 
+(csuba g x2 d1)).(\lambda (H15: (arity g x2 x3 (asucc g x4))).(\lambda (H16: 
+(arity g d1 u1 x4)).(or3_intro1 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead 
+x0 (Bind Void) x1) (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 (S 
+n) O (CHead x0 (Bind Void) x1) (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))))) (ex4_3_intro C T 
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x 
-(Bind Abbr) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop (S n) O (CHead x0 (Bind Void) x1) (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)))) x2 x3 x4 
+(drop_drop (Bind Void) n x0 (CHead x2 (Bind Abst) x3) H13 x1) H14 H15 
+H16))))))))) H12)) (\lambda (H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop n O x0 (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 
+n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(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 (S n) O (CHead x0 
+(Bind Void) x1) (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)))) x0 x1 x2 (drop_drop (Bind Abbr) n 
-x (CHead x0 (Bind Abst) x1) H18 t) H14 H15 H16))))))))))) H12)) H11)) c2 
-H9)))) H8)) (\lambda (H8: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: 
-T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\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 c t a)))))).(ex4_3_ind C T A 
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind 
-Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 
-c)))) (\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 c t a)))) 
-(or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) 
+(_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void) 
+x3))).(\lambda (H14: (csuba g x2 d1)).(or3_intro2 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (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 (S n) 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)))))) 
-(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H9: (eq C c2 
-(CHead x0 (Bind Abst) x1))).(\lambda (H10: (csuba g x0 c)).(\lambda (_: 
-(arity g x0 x1 (asucc g x2))).(\lambda (_: (arity g c t x2)).(eq_ind_r C 
-(CHead x0 (Bind Abst) x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop 
+(u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead 
+x0 (Bind Void) x1) (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).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 (drop_drop (Bind 
+Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12)) H11)) c2 H9))))) 
+H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abst) t))).(\lambda 
+(H6: (drop (r (Bind Abst) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def 
+(csuba_gen_abst_rev g c c2 t H5) in (let H7 \def H_x in (or_ind (ex2 C 
+(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba 
+g d2 c))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c)))) (or3 
+(ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H8: 
+(ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: 
+C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind 
+Abst) t))) (\lambda (d2: C).(csuba g d2 c)) (or3 (ex2 C (\lambda (d2: 
+C).(drop (S n) 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 (S 
+n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq 
+C c2 (CHead x (Bind Abst) t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C 
+(CHead x (Bind Abst) t) (\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop 
 (S n) O c0 (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 (S n) O 
 c0 (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))))))) (let H13 \def (H c d1 u1 H6 g x0 H10) in 
-(or_ind (ex2 C (\lambda (d2: C).(drop n O x0 (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 n O x0 (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))))) (or (ex2 C 
-(\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (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 (S n) O (CHead x0 (Bind Abst) x1) 
-(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)))))) (\lambda (H14: (ex2 C (\lambda (d2: C).(drop n 
-O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind 
-C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
-C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind 
-Abst) x1) (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 (S n) O 
-(CHead x0 (Bind Abst) x1) (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)))))) (\lambda (x: 
-C).(\lambda (H15: (drop n O x0 (CHead x (Bind Abbr) u1))).(\lambda (H16: 
-(csuba g x d1)).(let H17 \def (refl_equal nat (r (Bind Abst) n)) in (let H18 
-\def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x0 (CHead x (Bind Abbr) 
-u1))) H15 (r (Bind Abst) n) H17) in (or_introl (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1)))))) (let H11 \def (H c d1 u1 H6 g x H10) in (or3_ind 
+(ex2 C (\lambda (d2: C).(drop n O x (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 (S n) O (CHead x0 (Bind Abst) x1) (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))))) 
-(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead 
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Bind 
-Abst) n x0 (CHead x (Bind Abbr) u1) H18 x1) H16))))))) H14)) (\lambda (H14: 
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 
-(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)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: 
-T).(\lambda (_: A).(drop n O x0 (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)))) (or (ex2 C 
-(\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (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 (S n) O (CHead x0 (Bind Abst) x1) 
-(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)))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: 
-A).(\lambda (H15: (drop n O x0 (CHead x3 (Bind Abst) x4))).(\lambda (H16: 
-(csuba g x3 d1)).(\lambda (H17: (arity g x3 x4 (asucc g x5))).(\lambda (H18: 
-(arity g d1 u1 x5)).(let H19 \def (refl_equal nat (r (Bind Abst) n)) in (let 
-H20 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x0 (CHead x3 (Bind Abst) 
-x4))) H15 (r (Bind Abst) n) H19) in (or_intror (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
+(_: A).(drop n O x (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 n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S 
+n) O (CHead x (Bind Abst) t) (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 (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u2))))) 
+(_: A).(drop (S n) O (CHead x (Bind Abst) t) (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))))) 
-(ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S 
-n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 
+C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: 
+C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) 
+(or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (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 (S n) O (CHead x (Bind Abst) 
+t) (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 (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abbr) u1))).(\lambda (H14: 
+(csuba g x0 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x 
+(Bind Abst) t) (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 (S n) O 
+(CHead x (Bind Abst) t) (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)))) x3 x4 x5 
-(drop_drop (Bind Abst) n x0 (CHead x3 (Bind Abst) x4) H20 x1) H16 H17 
-H18))))))))))) H14)) H13)) c2 H9)))))))) H8)) H7))))) (\lambda (H5: (csuba g 
-c2 (CHead c (Bind Abst) t))).(\lambda (H6: (drop (r (Bind Abst) n) O c (CHead 
-d1 (Bind Abbr) u1))).(let H_x \def (csuba_gen_abst_rev g c c2 t H5) in (let 
-H7 \def H_x in (ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) 
-t))) (\lambda (d2: C).(csuba g d2 c)) (or (ex2 C (\lambda (d2: C).(drop (S n) 
-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 (S n) 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)))))) (\lambda (x: C).(\lambda (H8: (eq C c2 (CHead x 
-(Bind Abst) t))).(\lambda (H9: (csuba g x c)).(eq_ind_r C (CHead x (Bind 
-Abst) t) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H10 \def (H c d1 u1 H6 g x H9) in (or_ind (ex2 C (\lambda 
-(d2: C).(drop n O x (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 n 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) 
+(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop 
+(Bind Abst) n x (CHead x0 (Bind Abbr) u1) H13 t) H14))))) H12)) (\lambda 
+(H12: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n 
 O x (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))))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead 
-x (Bind Abst) t) (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 (S 
-n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+(a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: 
+T).(\lambda (_: A).(drop n O x (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)))))) (\lambda (H11: 
-(ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
-C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind 
-Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: 
-C).(drop (S n) O (CHead x (Bind Abst) t) (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 (S n) O (CHead x (Bind Abst) t) (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)))))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0 (Bind Abbr) 
-u1))).(\lambda (H13: (csuba g x0 d1)).(let H14 \def (refl_equal nat (r (Bind 
-Abst) n)) in (let H15 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x 
-(CHead x0 (Bind Abbr) u1))) H12 (r (Bind Abst) n) H14) in (or_introl (ex2 C 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C 
 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (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 (S n) O (CHead x (Bind Abst) t) 
 (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))))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O 
-(CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g 
-d2 d1)) x0 (drop_drop (Bind Abst) n x (CHead x0 (Bind Abbr) u1) H15 t) 
-H13))))))) H11)) (\lambda (H11: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: 
-T).(\lambda (_: A).(drop n O x (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)))))).(ex4_3_ind C T 
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (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)))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) 
-(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H13: (drop n O x (CHead x0 
+(Bind Abst) x1))).(\lambda (H14: (csuba g x0 d1)).(\lambda (H15: (arity g x0 
+x1 (asucc g x2))).(\lambda (H16: (arity g d1 u1 x2)).(or3_intro1 (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (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 (S n) O (CHead x (Bind Abst) t) 
+(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 (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A 
 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x 
 (Bind Abst) t) (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)))))) (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (x2: A).(\lambda (H12: (drop n O x (CHead x0 (Bind Abst) 
-x1))).(\lambda (H13: (csuba g x0 d1)).(\lambda (H14: (arity g x0 x1 (asucc g 
-x2))).(\lambda (H15: (arity g d1 u1 x2)).(let H16 \def (refl_equal nat (r 
-(Bind Abst) n)) in (let H17 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O 
-x (CHead x0 (Bind Abst) x1))) H12 (r (Bind Abst) n) H16) in (or_intror (ex2 C 
+(_: T).(\lambda (a: A).(arity g d1 u1 a)))) x0 x1 x2 (drop_drop (Bind Abst) n 
+x (CHead x0 (Bind Abst) x1) H13 t) H14 H15 H16))))))))) H12)) (\lambda (H12: 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (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 n O x (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C 
 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (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 (S n) O (CHead x (Bind Abst) t) 
 (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))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda 
-(u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead x0 (Bind Void) 
+x1))).(\lambda (H14: (csuba g x0 d1)).(or3_intro2 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x (Bind Abst) t) (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 (S n) O (CHead x (Bind Abst) t) (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)))) x0 x1 x2 (drop_drop (Bind Abst) n x (CHead x0 (Bind Abst) x1) H17 t) 
-H13 H14 H15))))))))))) H11)) H10)) c2 H8)))) H7))))) (\lambda (H5: (csuba g 
-c2 (CHead c (Bind Void) t))).(\lambda (H6: (drop (r (Bind Void) n) O c (CHead 
-d1 (Bind Abbr) u1))).(let H_x \def (csuba_gen_void_rev g c c2 t H5) in (let 
-H7 \def H_x in (ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Void) 
-t))) (\lambda (d2: C).(csuba g d2 c)) (or (ex2 C (\lambda (d2: C).(drop (S n) 
-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 (S n) 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)))))) (\lambda (x: C).(\lambda (H8: (eq C c2 (CHead x 
-(Bind Void) t))).(\lambda (H9: (csuba g x c)).(eq_ind_r C (CHead x (Bind 
-Void) t) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead 
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda 
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x 
+(Bind Abst) t) (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).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_drop (Bind 
+Abst) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12)) H11)) c2 H9)))) 
+H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c))) (or3 
+(ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H9: (eq C c2 (CHead x0 (Bind Void) 
+x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r C (CHead x0 (Bind Void) x1) 
+(\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop (S n) O c0 (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 (S n) O c0 (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))))))) (let H10 \def (H c d1 u1 H6 g x H9) in (or_ind (ex2 C (\lambda 
-(d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))))) (let H11 \def (H c d1 u1 H6 g x0 H10) in (or3_ind (ex2 C (\lambda 
+(d2: C).(drop n O x0 (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 n 
-O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda 
+O x0 (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))))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead 
-x (Bind Void) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
+(Bind Void) x1) (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 (S 
-n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
+n) O (CHead x0 (Bind Void) x1) (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)))))) (\lambda (H11: 
-(ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T 
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: 
+C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) 
+(or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) 
+x1) (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 (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda 
+(H13: (drop n O x0 (CHead x (Bind Abbr) u1))).(\lambda (H14: (csuba g x 
+d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) 
+x1) (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 (S n) O (CHead x0 
+(Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Bind Void) n x0 
+(CHead x (Bind Abbr) u1) H13 x1) H14))))) H12)) (\lambda (H12: (ex4_3 C T A 
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 (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)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop n O x0 (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)))) (or3 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead 
+x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: 
+A).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Abst) x3))).(\lambda (H14: 
+(csuba g x2 d1)).(\lambda (H15: (arity g x2 x3 (asucc g x4))).(\lambda (H16: 
+(arity g d1 u1 x4)).(or3_intro1 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead 
+x0 (Bind Void) x1) (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 (S 
+n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) x1) 
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop (S n) O (CHead x0 (Bind Void) x1) (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)))) x2 x3 x4 
+(drop_drop (Bind Void) n x0 (CHead x2 (Bind Abst) x3) H13 x1) H14 H15 
+H16))))))))) H12)) (\lambda (H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop n O x0 (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 
+n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) 
+(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 (S n) O (CHead x0 
+(Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda 
+(x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void) 
+x3))).(\lambda (H14: (csuba g x2 d1)).(or3_intro2 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead x0 (Bind Void) x1) (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 (S n) O (CHead 
+x0 (Bind Void) x1) (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).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 (drop_drop (Bind 
+Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12)) H11)) c2 H9))))) 
+H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Void) t))).(\lambda 
+(H6: (drop (r (Bind Void) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def 
+(csuba_gen_void_rev g c c2 t H5) in (let H7 \def H_x in (ex2_ind C (\lambda 
+(d2: C).(eq C c2 (CHead d2 (Bind Void) t))) (\lambda (d2: C).(csuba g d2 c)) 
+(or3 (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: 
+C).(\lambda (H8: (eq C c2 (CHead x (Bind Void) t))).(\lambda (H9: (csuba g x 
+c)).(eq_ind_r C (CHead x (Bind Void) t) (\lambda (c0: C).(or3 (ex2 C (\lambda 
+(d2: C).(drop (S n) O c0 (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 (S n) O c0 (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 (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H10 \def (H c d1 u1 H6 g x 
+H9) in (or3_ind (ex2 C (\lambda (d2: C).(drop n O x (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 n O x (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 n O x (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x (Bind Void) t) 
+(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 (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H11: (ex2 C 
+(\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: 
 C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind 
-Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2: 
 C).(drop (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x (Bind Void) t) (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)))))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0 (Bind Abbr) 
-u1))).(\lambda (H13: (csuba g x0 d1)).(let H14 \def (refl_equal nat (r (Bind 
-Abst) n)) in (let H15 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x 
-(CHead x0 (Bind Abbr) u1))) H12 (r (Bind Abst) n) H14) in (or_introl (ex2 C 
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x 
+(Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0 
+(Bind Abbr) u1))).(\lambda (H13: (csuba g x0 d1)).(or3_intro0 (ex2 C (\lambda 
+(d2: C).(drop (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x 
+(Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x 
+(Bind Void) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) 
+x0 (drop_drop (Bind Void) n x (CHead x0 (Bind Abbr) u1) H12 t) H13))))) H11)) 
+(\lambda (H11: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop n O x (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)))))).(ex4_3_ind C T A (\lambda (d2: 
+C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (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)))) (or3 
+(ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x (Bind Void) t) 
+(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 (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H12: (drop n O x (CHead x0 
+(Bind Abst) x1))).(\lambda (H13: (csuba g x0 d1)).(\lambda (H14: (arity g x0 
+x1 (asucc g x2))).(\lambda (H15: (arity g d1 u1 x2)).(or3_intro1 (ex2 C 
 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x (Bind Void) t) 
 (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))))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O 
-(CHead x (Bind Void) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g 
-d2 d1)) x0 (drop_drop (Bind Void) n x (CHead x0 (Bind Abbr) u1) H15 t) 
-H13))))))) H11)) (\lambda (H11: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: 
-T).(\lambda (_: A).(drop n O x (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)))))).(ex4_3_ind C T 
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (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)))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) 
-(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A 
 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x 
 (Bind Void) t) (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)))))) (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (x2: A).(\lambda (H12: (drop n O x (CHead x0 (Bind Abst) 
-x1))).(\lambda (H13: (csuba g x0 d1)).(\lambda (H14: (arity g x0 x1 (asucc g 
-x2))).(\lambda (H15: (arity g d1 u1 x2)).(let H16 \def (refl_equal nat (r 
-(Bind Abst) n)) in (let H17 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O 
-x (CHead x0 (Bind Abst) x1))) H12 (r (Bind Abst) n) H16) in (or_intror (ex2 C 
+(_: T).(\lambda (a: A).(arity g d1 u1 a)))) x0 x1 x2 (drop_drop (Bind Void) n 
+x (CHead x0 (Bind Abst) x1) H12 t) H13 H14 H15))))))))) H11)) (\lambda (H11: 
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (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 n O x (CHead d2 (Bind Void) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C 
 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x (Bind Void) t) 
 (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))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda 
-(u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H12: (drop n O x (CHead x0 (Bind Void) 
+x1))).(\lambda (H13: (csuba g x0 d1)).(or3_intro2 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x (Bind Void) t) (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 (S n) O (CHead x (Bind Void) t) (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)))) x0 x1 x2 (drop_drop (Bind Void) n x (CHead x0 (Bind Abst) x1) H17 t) 
-H13 H14 H15))))))))))) H11)) H10)) c2 H8)))) H7))))) b H3 H4)))) (\lambda (f: 
-F).(\lambda (H3: (csuba g c2 (CHead c (Flat f) t))).(\lambda (H4: (drop (r 
-(Flat f) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def (csuba_gen_flat_rev 
-g c c2 t f H3) in (let H5 \def H_x in (ex2_2_ind C T (\lambda (d2: 
-C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: 
-C).(\lambda (_: T).(csuba g d2 c))) (or (ex2 C (\lambda (d2: C).(drop (S n) 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 (S n) 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)))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: 
-(eq C c2 (CHead x0 (Flat f) x1))).(\lambda (H7: (csuba g x0 c)).(eq_ind_r C 
-(CHead x0 (Flat f) x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S 
-n) O c0 (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 (S n) O c0 
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x 
+(Bind Void) t) (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).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2)))) 
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_drop (Bind 
+Void) n x (CHead x0 (Bind Void) x1) H12 t) H13)))))) H11)) H10)) c2 H8)))) 
+H7))))) b H3 H4)))) (\lambda (f: F).(\lambda (H3: (csuba g c2 (CHead c (Flat 
+f) t))).(\lambda (H4: (drop (r (Flat f) n) O c (CHead d1 (Bind Abbr) 
+u1))).(let H_x \def (csuba_gen_flat_rev g c c2 t f H3) in (let H5 \def H_x in 
+(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) 
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c))) (or3 (ex2 C (\lambda 
+(d2: C).(drop (S n) 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 (S n) 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 (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: 
+T).(\lambda (H6: (eq C c2 (CHead x0 (Flat f) x1))).(\lambda (H7: (csuba g x0 
+c)).(eq_ind_r C (CHead x0 (Flat f) x1) (\lambda (c0: C).(or3 (ex2 C (\lambda 
+(d2: C).(drop (S n) O c0 (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 (S n) O c0 (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 (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H8 \def (H0 d1 u1 H4 g x0 
+H7) in (or3_ind (ex2 C (\lambda (d2: C).(drop (S n) O x0 (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 (S n) O x0 (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 (S n) O x0 (CHead d2 (Bind 
+Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C 
+(\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) 
 (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))))))) (let H8 \def (H0 d1 u1 H4 g x0 H7) in (or_ind 
-(ex2 C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abbr) u1))) (\lambda 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H9: (ex2 C (\lambda 
+(d2: C).(drop (S n) O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba 
+g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind 
+Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) 
+x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1))))) (\lambda (x: C).(\lambda (H10: (drop (S n) O x0 (CHead x (Bind Abbr) 
+u1))).(\lambda (H11: (csuba g x d1)).(or3_intro0 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) 
+x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) 
+(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop 
+(Flat f) n x0 (CHead x (Bind Abbr) u1) H10 x1) H11))))) H9)) (\lambda (H9: 
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O 
+x0 (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)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: 
 T).(\lambda (_: A).(drop (S n) O x0 (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))))) (or (ex2 C 
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C 
 (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) 
 (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)))))) (\lambda (H9: (ex2 C (\lambda (d2: C).(drop (S 
-n) O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 
-d1)))).(ex2_ind C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abbr) 
-u1))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S 
-n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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)))))) 
-(\lambda (x: C).(\lambda (H10: (drop (S n) O x0 (CHead x (Bind Abbr) 
-u1))).(\lambda (H11: (csuba g x d1)).(or_introl (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u2))))) 
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (x3: 
+T).(\lambda (x4: A).(\lambda (H10: (drop (S n) O x0 (CHead x2 (Bind Abst) 
+x3))).(\lambda (H11: (csuba g x2 d1)).(\lambda (H12: (arity g x2 x3 (asucc g 
+x4))).(\lambda (H13: (arity g d1 u1 x4)).(or3_intro1 (ex2 C (\lambda (d2: 
+C).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) 
+x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 
+d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(drop (S n) O (CHead x0 (Flat f) x1) (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))))) 
-(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Flat f) n 
-x0 (CHead x (Bind Abbr) u1) H10 x1) H11))))) H9)) (\lambda (H9: (ex4_3 C T A 
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O x0 (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 
+(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x2 x3 x4 
+(drop_drop (Flat f) n x0 (CHead x2 (Bind Abst) x3) H10 x1) H11 H12 
+H13))))))))) H9)) (\lambda (H9: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(drop (S n) O x0 (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 (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda 
+(_: T).(csuba g d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 
+(Flat f) x1) (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 (S n) O 
+(CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (CHead 
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) 
+(\lambda (x2: C).(\lambda (x3: T).(\lambda (H10: (drop (S n) O x0 (CHead x2 
+(Bind Void) x3))).(\lambda (H11: (csuba g x2 d1)).(or3_intro2 (ex2 C (\lambda 
+(d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
-A).(drop (S n) O x0 (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)))) (or (ex2 C (\lambda (d2: C).(drop 
-(S n) O (CHead x0 (Flat f) x1) (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 (S n) O (CHead x0 (Flat f) x1) (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)))))) 
-(\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: A).(\lambda (H10: (drop (S n) 
-O x0 (CHead x2 (Bind Abst) x3))).(\lambda (H11: (csuba g x2 d1)).(\lambda 
-(H12: (arity g x2 x3 (asucc g x4))).(\lambda (H13: (arity g d1 u1 
-x4)).(or_intror (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) 
-(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 (S n) O (CHead x0 
-(Flat f) x1) (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))))) (ex4_3_intro C T A (\lambda (d2: 
-C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1) 
-(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)))) x2 x3 x4 (drop_drop (Flat f) n x0 (CHead x2 (Bind 
-Abst) x3) H10 x1) H11 H12 H13))))))))) H9)) H8)) c2 H6))))) H5)))))) k H2 
-(drop_gen_drop k c (CHead d1 (Bind Abbr) u1) t n H1)))))))))))) c1)))) i).
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead 
+x0 (Flat f) x1) (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).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda 
+(d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 (drop_drop (Flat f) n x0 
+(CHead x2 (Bind Void) x3) H10 x1) H11)))))) H9)) H8)) c2 H6))))) H5)))))) k 
+H2 (drop_gen_drop k c (CHead d1 (Bind Abbr) u1) t n H1)))))))))))) c1)))) i).