C).(\lambda (H1: (csubt g c0 c3)).(\lambda (_: ((\forall (d1: C).(\forall (u:
T).((drop (S n0) O c0 (CHead d1 (Flat f) u)) \to (ex2 C (\lambda (d2:
C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Flat f)
-u))))))))).(\lambda (u: T).(\lambda (t: T).(\lambda (_: (ty3 g c3 u
-t)).(\lambda (d1: C).(\lambda (u0: T).(\lambda (H4: (drop (S n0) O (CHead c0
-(Bind Abst) t) (CHead d1 (Flat f) u0))).(ex2_ind C (\lambda (d2: C).(csubt g
-d1 d2)) (\lambda (d2: C).(drop n0 O c3 (CHead d2 (Flat f) u0))) (ex2 C
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3
-(Bind Abbr) u) (CHead d2 (Flat f) u0)))) (\lambda (x: C).(\lambda (H5: (csubt
-g d1 x)).(\lambda (H6: (drop n0 O c3 (CHead x (Flat f) u0))).(ex_intro2 C
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3
-(Bind Abbr) u) (CHead d2 (Flat f) u0))) x H5 (drop_drop (Bind Abbr) n0 c3
-(CHead x (Flat f) u0) H6 u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop (Bind Abst)
-c0 (CHead d1 (Flat f) u0) t n0 H4))))))))))))) c1 c2 H0)))))) n))).
+u))))))))).(\lambda (u: T).(\lambda (t: T).(\lambda (_: (ty3 g c0 u
+t)).(\lambda (_: (ty3 g c3 u t)).(\lambda (d1: C).(\lambda (u0: T).(\lambda
+(H5: (drop (S n0) O (CHead c0 (Bind Abst) t) (CHead d1 (Flat f)
+u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0
+O c3 (CHead d2 (Flat f) u0))) (ex2 C (\lambda (d2: C).(csubt g d1 d2))
+(\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Flat f)
+u0)))) (\lambda (x: C).(\lambda (H6: (csubt g d1 x)).(\lambda (H7: (drop n0 O
+c3 (CHead x (Flat f) u0))).(ex_intro2 C (\lambda (d2: C).(csubt g d1 d2))
+(\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Flat f)
+u0))) x H6 (drop_drop (Bind Abbr) n0 c3 (CHead x (Flat f) u0) H7 u))))) (H c0
+c3 H1 d1 u0 (drop_gen_drop (Bind Abst) c0 (CHead d1 (Flat f) u0) t n0
+H5)))))))))))))) c1 c2 H0)))))) n))).
theorem csubt_drop_abbr:
\forall (g: G).(\forall (n: nat).(\forall (c1: C).(\forall (c2: C).((csubt g
C).(\forall (u: T).((drop (S n0) O c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C
(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O c3 (CHead
d2 (Bind Abbr) u))))))))).(\lambda (u: T).(\lambda (t: T).(\lambda (_: (ty3 g
-c3 u t)).(\lambda (d1: C).(\lambda (u0: T).(\lambda (H4: (drop (S n0) O
-(CHead c0 (Bind Abst) t) (CHead d1 (Bind Abbr) u0))).(ex2_ind C (\lambda (d2:
-C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0 O c3 (CHead d2 (Bind Abbr)
-u0))) (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0)
-O (CHead c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0)))) (\lambda (x:
-C).(\lambda (H5: (csubt g d1 x)).(\lambda (H6: (drop n0 O c3 (CHead x (Bind
-Abbr) u0))).(ex_intro2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
-C).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0))) x H5
-(drop_drop (Bind Abbr) n0 c3 (CHead x (Bind Abbr) u0) H6 u))))) (H c0 c3 H1
-d1 u0 (drop_gen_drop (Bind Abst) c0 (CHead d1 (Bind Abbr) u0) t n0
-H4))))))))))))) c1 c2 H0)))))) n)).
+c0 u t)).(\lambda (_: (ty3 g c3 u t)).(\lambda (d1: C).(\lambda (u0:
+T).(\lambda (H5: (drop (S n0) O (CHead c0 (Bind Abst) t) (CHead d1 (Bind
+Abbr) u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
+C).(drop n0 O c3 (CHead d2 (Bind Abbr) u0))) (ex2 C (\lambda (d2: C).(csubt g
+d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2
+(Bind Abbr) u0)))) (\lambda (x: C).(\lambda (H6: (csubt g d1 x)).(\lambda
+(H7: (drop n0 O c3 (CHead x (Bind Abbr) u0))).(ex_intro2 C (\lambda (d2:
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind Abbr) u)
+(CHead d2 (Bind Abbr) u0))) x H6 (drop_drop (Bind Abbr) n0 c3 (CHead x (Bind
+Abbr) u0) H7 u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop (Bind Abst) c0 (CHead d1
+(Bind Abbr) u0) t n0 H5)))))))))))))) c1 c2 H0)))))) n)).
theorem csubt_drop_abst:
\forall (g: G).(\forall (n: nat).(\forall (c1: C).(\forall (c2: C).((csubt g
c1 c2) \to (\forall (d1: C).(\forall (t: T).((drop n O c1 (CHead d1 (Bind
Abst) t)) \to (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
-C).(drop n O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2:
+C).(drop n O c2 (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2:
C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop n
-O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u
-t))))))))))))
+O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u
+t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))))))))))
\def
\lambda (g: G).(\lambda (n: nat).(nat_ind (\lambda (n0: nat).(\forall (c1:
C).(\forall (c2: C).((csubt g c1 c2) \to (\forall (d1: C).(\forall (t:
T).((drop n0 O c1 (CHead d1 (Bind Abst) t)) \to (or (ex2 C (\lambda (d2:
C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0 O c2 (CHead d2 (Bind Abst)
-t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda
+t)))) (ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda
(d2: C).(\lambda (u: T).(drop n0 O c2 (CHead d2 (Bind Abbr) u)))) (\lambda
-(d2: C).(\lambda (u: T).(ty3 g d2 u t)))))))))))) (\lambda (c1: C).(\lambda
-(c2: C).(\lambda (H: (csubt g c1 c2)).(\lambda (d1: C).(\lambda (t:
-T).(\lambda (H0: (drop O O c1 (CHead d1 (Bind Abst) t))).(let H1 \def (eq_ind
-C c1 (\lambda (c: C).(csubt g c c2)) H (CHead d1 (Bind Abst) t)
-(drop_gen_refl c1 (CHead d1 (Bind Abst) t) H0)) in (let H2 \def
-(csubt_gen_abst g d1 c2 t H1) in (or_ind (ex2 C (\lambda (e2: C).(eq C c2
-(CHead e2 (Bind Abst) t))) (\lambda (e2: C).(csubt g d1 e2))) (ex3_2 C T
-(\lambda (e2: C).(\lambda (v2: T).(eq C c2 (CHead e2 (Bind Abbr) v2))))
-(\lambda (e2: C).(\lambda (_: T).(csubt g d1 e2))) (\lambda (e2: C).(\lambda
-(v2: T).(ty3 g e2 v2 t)))) (or (ex2 C (\lambda (d2: C).(csubt g d1 d2))
-(\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda
-(d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u:
-T).(drop O O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u:
-T).(ty3 g d2 u t))))) (\lambda (H3: (ex2 C (\lambda (e2: C).(eq C c2 (CHead
-e2 (Bind Abst) t))) (\lambda (e2: C).(csubt g d1 e2)))).(ex2_ind C (\lambda
-(e2: C).(eq C c2 (CHead e2 (Bind Abst) t))) (\lambda (e2: C).(csubt g d1 e2))
-(or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c2
-(CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_:
-T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O c2 (CHead d2
-(Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t)))))
+(_: C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda (u: T).(ty3
+g d2 u t)))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubt g
+c1 c2)).(\lambda (d1: C).(\lambda (t: T).(\lambda (H0: (drop O O c1 (CHead d1
+(Bind Abst) t))).(let H1 \def (eq_ind C c1 (\lambda (c: C).(csubt g c c2)) H
+(CHead d1 (Bind Abst) t) (drop_gen_refl c1 (CHead d1 (Bind Abst) t) H0)) in
+(let H2 \def (csubt_gen_abst g d1 c2 t H1) in (or_ind (ex2 C (\lambda (e2:
+C).(eq C c2 (CHead e2 (Bind Abst) t))) (\lambda (e2: C).(csubt g d1 e2)))
+(ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C c2 (CHead e2 (Bind Abbr)
+v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g d1 e2))) (\lambda (_:
+C).(\lambda (v2: T).(ty3 g d1 v2 t))) (\lambda (e2: C).(\lambda (v2: T).(ty3
+g e2 v2 t)))) (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
+C).(drop O O c2 (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2:
+C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop O
+O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u
+t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))) (\lambda (H3: (ex2 C
+(\lambda (e2: C).(eq C c2 (CHead e2 (Bind Abst) t))) (\lambda (e2: C).(csubt
+g d1 e2)))).(ex2_ind C (\lambda (e2: C).(eq C c2 (CHead e2 (Bind Abst) t)))
+(\lambda (e2: C).(csubt g d1 e2)) (or (ex2 C (\lambda (d2: C).(csubt g d1
+d2)) (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abst) t)))) (ex4_2 C T
+(\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda
+(u: T).(drop O O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda (u:
+T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t)))))
(\lambda (x: C).(\lambda (H4: (eq C c2 (CHead x (Bind Abst) t))).(\lambda
(H5: (csubt g d1 x)).(eq_ind_r C (CHead x (Bind Abst) t) (\lambda (c: C).(or
(ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c (CHead
-d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1
+d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1
d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O c (CHead d2 (Bind Abbr)
-u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t)))))) (or_introl (ex2 C
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O (CHead x (Bind
-Abst) t) (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_:
-T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O (CHead x
-(Bind Abst) t) (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u:
-T).(ty3 g d2 u t)))) (ex_intro2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda
-(d2: C).(drop O O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) t))) x H5
-(drop_refl (CHead x (Bind Abst) t)))) c2 H4)))) H3)) (\lambda (H3: (ex3_2 C T
-(\lambda (e2: C).(\lambda (v2: T).(eq C c2 (CHead e2 (Bind Abbr) v2))))
-(\lambda (e2: C).(\lambda (_: T).(csubt g d1 e2))) (\lambda (e2: C).(\lambda
-(v2: T).(ty3 g e2 v2 t))))).(ex3_2_ind C T (\lambda (e2: C).(\lambda (v2:
+u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2:
+C).(\lambda (u: T).(ty3 g d2 u t)))))) (or_introl (ex2 C (\lambda (d2:
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O (CHead x (Bind Abst) t) (CHead
+d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1
+d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O (CHead x (Bind Abst) t)
+(CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u t)))
+(\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t)))) (ex_intro2 C (\lambda (d2:
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O (CHead x (Bind Abst) t) (CHead
+d2 (Bind Abst) t))) x H5 (drop_refl (CHead x (Bind Abst) t)))) c2 H4)))) H3))
+(\lambda (H3: (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C c2 (CHead e2
+(Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g d1 e2)))
+(\lambda (_: C).(\lambda (v2: T).(ty3 g d1 v2 t))) (\lambda (e2: C).(\lambda
+(v2: T).(ty3 g e2 v2 t))))).(ex4_2_ind C T (\lambda (e2: C).(\lambda (v2:
T).(eq C c2 (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_:
-T).(csubt g d1 e2))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 t))) (or
-(ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c2 (CHead
-d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1
-d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O c2 (CHead d2 (Bind Abbr)
-u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))) (\lambda (x0:
-C).(\lambda (x1: T).(\lambda (H4: (eq C c2 (CHead x0 (Bind Abbr)
-x1))).(\lambda (H5: (csubt g d1 x0)).(\lambda (H6: (ty3 g x0 x1 t)).(eq_ind_r
-C (CHead x0 (Bind Abbr) x1) (\lambda (c: C).(or (ex2 C (\lambda (d2:
-C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c (CHead d2 (Bind Abst) t))))
-(ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2:
-C).(\lambda (u: T).(drop O O c (CHead d2 (Bind Abbr) u)))) (\lambda (d2:
-C).(\lambda (u: T).(ty3 g d2 u t)))))) (or_intror (ex2 C (\lambda (d2:
-C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O (CHead x0 (Bind Abbr) x1)
-(CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_:
-T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O (CHead x0
-(Bind Abbr) x1) (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u:
-T).(ty3 g d2 u t)))) (ex3_2_intro C T (\lambda (d2: C).(\lambda (_: T).(csubt
-g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O (CHead x0 (Bind Abbr)
-x1) (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u
-t))) x0 x1 H5 (drop_refl (CHead x0 (Bind Abbr) x1)) H6)) c2 H4)))))) H3))
-H2))))))))) (\lambda (n0: nat).(\lambda (H: ((\forall (c1: C).(\forall (c2:
-C).((csubt g c1 c2) \to (\forall (d1: C).(\forall (t: T).((drop n0 O c1
+T).(csubt g d1 e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g d1 v2 t)))
+(\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 t))) (or (ex2 C (\lambda (d2:
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abst) t))))
+(ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2:
+C).(\lambda (u: T).(drop O O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (_:
+C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g
+d2 u t))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H4: (eq C c2 (CHead
+x0 (Bind Abbr) x1))).(\lambda (H5: (csubt g d1 x0)).(\lambda (H6: (ty3 g d1
+x1 t)).(\lambda (H7: (ty3 g x0 x1 t)).(eq_ind_r C (CHead x0 (Bind Abbr) x1)
+(\lambda (c: C).(or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
+C).(drop O O c (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2:
+C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop O
+O c (CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u
+t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t)))))) (or_intror (ex2 C
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O (CHead x0 (Bind
+Abbr) x1) (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2: C).(\lambda
+(_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop O O (CHead x0
+(Bind Abbr) x1) (CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda (u:
+T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))
+(ex4_2_intro C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda
+(d2: C).(\lambda (u: T).(drop O O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind
+Abbr) u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2:
+C).(\lambda (u: T).(ty3 g d2 u t))) x0 x1 H5 (drop_refl (CHead x0 (Bind Abbr)
+x1)) H6 H7)) c2 H4))))))) H3)) H2))))))))) (\lambda (n0: nat).(\lambda (H:
+((\forall (c1: C).(\forall (c2: C).((csubt g c1 c2) \to (\forall (d1:
+C).(\forall (t: T).((drop n0 O c1 (CHead d1 (Bind Abst) t)) \to (or (ex2 C
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0 O c2 (CHead d2
+(Bind Abst) t)))) (ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1
+d2))) (\lambda (d2: C).(\lambda (u: T).(drop n0 O c2 (CHead d2 (Bind Abbr)
+u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2:
+C).(\lambda (u: T).(ty3 g d2 u t))))))))))))).(\lambda (c1: C).(\lambda (c2:
+C).(\lambda (H0: (csubt g c1 c2)).(csubt_ind g (\lambda (c: C).(\lambda (c0:
+C).(\forall (d1: C).(\forall (t: T).((drop (S n0) O c (CHead d1 (Bind Abst)
+t)) \to (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop
+(S n0) O c0 (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2: C).(\lambda
+(_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(drop (S n0) O c0
+(CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u t)))
+(\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t)))))))))) (\lambda (n1:
+nat).(\lambda (d1: C).(\lambda (t: T).(\lambda (H1: (drop (S n0) O (CSort n1)
+(CHead d1 (Bind Abst) t))).(and3_ind (eq C (CHead d1 (Bind Abst) t) (CSort
+n1)) (eq nat (S n0) O) (eq nat O O) (or (ex2 C (\lambda (d2: C).(csubt g d1
+d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abst) t))))
+(ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2:
+C).(\lambda (u: T).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abbr) u))))
+(\lambda (_: C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda
+(u: T).(ty3 g d2 u t))))) (\lambda (_: (eq C (CHead d1 (Bind Abst) t) (CSort
+n1))).(\lambda (H3: (eq nat (S n0) O)).(\lambda (_: (eq nat O O)).(let H5
+\def (eq_ind nat (S n0) (\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).(csubt g d1 d2)) (\lambda (d2:
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+T).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abbr) u)))) (\lambda (_:
+C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g
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+H1)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda (H1: (csubt g c0
+c3)).(\lambda (H2: ((\forall (d1: C).(\forall (t: T).((drop (S n0) O c0
(CHead d1 (Bind Abst) t)) \to (or (ex2 C (\lambda (d2: C).(csubt g d1 d2))
-(\lambda (d2: C).(drop n0 O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T
+(\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Bind Abst) t)))) (ex4_2 C T
(\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda
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-(ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O c0
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-\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2
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-t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda
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-T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2:
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-T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u0: T).(drop (S n0) O (CHead
-c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0)))) (\lambda (d2: C).(\lambda (u0:
-T).(ty3 g d2 u0 t0))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6:
-(csubt g d1 x0)).(\lambda (H7: (drop n0 O c3 (CHead x0 (Bind Abbr)
-x1))).(\lambda (H8: (ty3 g x0 x1 t0)).(or_intror (ex2 C (\lambda (d2:
+(S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0)))) (\lambda (_:
+C).(\lambda (u0: T).(ty3 g d1 u0 t0))) (\lambda (d2: C).(\lambda (u0: T).(ty3
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+(\lambda (d2: C).(drop n0 O c3 (CHead d2 (Bind Abst) t0))))).(ex2_ind C
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0 O c3 (CHead d2
+(Bind Abst) t0))) (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
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+(ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2:
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+Abbr) u0)))) (\lambda (_: C).(\lambda (u0: T).(ty3 g d1 u0 t0))) (\lambda
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+(csubt g d1 x)).(\lambda (H8: (drop n0 O c3 (CHead x (Bind Abst)
+t0))).(or_introl (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
+C).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Bind Abst) t0))))
+(ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2:
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C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind Abbr) u)
-(CHead d2 (Bind Abst) t0)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_:
-T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u0: T).(drop (S n0) O (CHead
-c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0)))) (\lambda (d2: C).(\lambda (u0:
-T).(ty3 g d2 u0 t0)))) (ex3_2_intro C T (\lambda (d2: C).(\lambda (_:
-T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u0: T).(drop (S n0) O (CHead
-c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0)))) (\lambda (d2: C).(\lambda (u0:
-T).(ty3 g d2 u0 t0))) x0 x1 H6 (drop_drop (Bind Abbr) n0 c3 (CHead x0 (Bind
-Abbr) x1) H7 u) H8))))))) H5)) (H c0 c3 H1 d1 t0 (drop_gen_drop (Bind Abst)
-c0 (CHead d1 (Bind Abst) t0) t n0 H4))))))))))))) c1 c2 H0)))))) n)).
+(CHead d2 (Bind Abst) t0))) x H7 (drop_drop (Bind Abbr) n0 c3 (CHead x (Bind
+Abst) t0) H8 u)))))) H6)) (\lambda (H6: (ex4_2 C T (\lambda (d2: C).(\lambda
+(_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u0: T).(drop n0 O c3
+(CHead d2 (Bind Abbr) u0)))) (\lambda (_: C).(\lambda (u0: T).(ty3 g d1 u0
+t0))) (\lambda (d2: C).(\lambda (u0: T).(ty3 g d2 u0 t0))))).(ex4_2_ind C T
+(\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda
+(u0: T).(drop n0 O c3 (CHead d2 (Bind Abbr) u0)))) (\lambda (_: C).(\lambda
+(u0: T).(ty3 g d1 u0 t0))) (\lambda (d2: C).(\lambda (u0: T).(ty3 g d2 u0
+t0))) (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S
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+(\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda
+(u0: T).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0))))
+(\lambda (_: C).(\lambda (u0: T).(ty3 g d1 u0 t0))) (\lambda (d2: C).(\lambda
+(u0: T).(ty3 g d2 u0 t0))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H7:
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+x1))).(\lambda (H9: (ty3 g d1 x1 t0)).(\lambda (H10: (ty3 g x0 x1
+t0)).(or_intror (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
+C).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Bind Abst) t0))))
+(ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2:
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+Abbr) u0)))) (\lambda (_: C).(\lambda (u0: T).(ty3 g d1 u0 t0))) (\lambda
+(d2: C).(\lambda (u0: T).(ty3 g d2 u0 t0)))) (ex4_2_intro C T (\lambda (d2:
+C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u0: T).(drop
+(S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 (Bind Abbr) u0)))) (\lambda (_:
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+g d2 u0 t0))) x0 x1 H7 (drop_drop (Bind Abbr) n0 c3 (CHead x0 (Bind Abbr) x1)
+H8 u) H9 H10)))))))) H6)) (H c0 c3 H1 d1 t0 (drop_gen_drop (Bind Abst) c0
+(CHead d1 (Bind Abst) t0) t n0 H5)))))))))))))) c1 c2 H0)))))) n)).