-(CHead d1 (Flat f) u) (drop_gen_refl c1 (CHead d1 (Flat f) u) H0)) in (let H2
-\def (match H1 in csubt return (\lambda (c: C).(\lambda (c0: C).(\lambda (_:
-(csubt ? c c0)).((eq C c (CHead d1 (Flat f) u)) \to ((eq C c0 c2) \to (ex2 C
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c2 (CHead d2
-(Flat f) u))))))))) with [(csubt_sort n0) \Rightarrow (\lambda (H2: (eq C
-(CSort n0) (CHead d1 (Flat f) u))).(\lambda (H3: (eq C (CSort n0) c2)).((let
-H4 \def (eq_ind C (CSort n0) (\lambda (e: C).(match e in C return (\lambda
-(_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow
-False])) I (CHead d1 (Flat f) u) H2) in (False_ind ((eq C (CSort n0) c2) \to
-(ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c2 (CHead
-d2 (Flat f) u))))) H4)) H3))) | (csubt_head c0 c3 H2 k u0) \Rightarrow
-(\lambda (H3: (eq C (CHead c0 k u0) (CHead d1 (Flat f) u))).(\lambda (H4: (eq
-C (CHead c3 k u0) c2)).((let H5 \def (f_equal C T (\lambda (e: C).(match e in
-C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ t)
-\Rightarrow t])) (CHead c0 k u0) (CHead d1 (Flat f) u) H3) in ((let H6 \def
-(f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K) with
-[(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c0 k u0)
-(CHead d1 (Flat f) u) H3) in ((let H7 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c0 |
-(CHead c _ _) \Rightarrow c])) (CHead c0 k u0) (CHead d1 (Flat f) u) H3) in
-(eq_ind C d1 (\lambda (c: C).((eq K k (Flat f)) \to ((eq T u0 u) \to ((eq C
-(CHead c3 k u0) c2) \to ((csubt g c c3) \to (ex2 C (\lambda (d2: C).(csubt g
-d1 d2)) (\lambda (d2: C).(drop O O c2 (CHead d2 (Flat f) u))))))))) (\lambda
-(H8: (eq K k (Flat f))).(eq_ind K (Flat f) (\lambda (k0: K).((eq T u0 u) \to
-((eq C (CHead c3 k0 u0) c2) \to ((csubt g d1 c3) \to (ex2 C (\lambda (d2:
-C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c2 (CHead d2 (Flat f)
-u)))))))) (\lambda (H9: (eq T u0 u)).(eq_ind T u (\lambda (t: T).((eq C
-(CHead c3 (Flat f) t) c2) \to ((csubt g d1 c3) \to (ex2 C (\lambda (d2:
-C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O c2 (CHead d2 (Flat f) u)))))))
-(\lambda (H10: (eq C (CHead c3 (Flat f) u) c2)).(eq_ind C (CHead c3 (Flat f)
-u) (\lambda (c: C).((csubt g d1 c3) \to (ex2 C (\lambda (d2: C).(csubt g d1
-d2)) (\lambda (d2: C).(drop O O c (CHead d2 (Flat f) u)))))) (\lambda (H11:
-(csubt g d1 c3)).(ex_intro2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
-C).(drop O O (CHead c3 (Flat f) u) (CHead d2 (Flat f) u))) c3 H11 (drop_refl
-(CHead c3 (Flat f) u)))) c2 H10)) u0 (sym_eq T u0 u H9))) k (sym_eq K k (Flat
-f) H8))) c0 (sym_eq C c0 d1 H7))) H6)) H5)) H4 H2))) | (csubt_void c0 c3 H2 b
-H3 u1 u2) \Rightarrow (\lambda (H4: (eq C (CHead c0 (Bind Void) u1) (CHead d1
-(Flat f) u))).(\lambda (H5: (eq C (CHead c3 (Bind b) u2) c2)).((let H6 \def
-(eq_ind C (CHead c0 (Bind Void) u1) (\lambda (e: C).(match e in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _)
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _)
-\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1 (Flat f) u)
-H4) in (False_ind ((eq C (CHead c3 (Bind b) u2) c2) \to ((csubt g c0 c3) \to
-((not (eq B b Void)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda
-(d2: C).(drop O O c2 (CHead d2 (Flat f) u))))))) H6)) H5 H2 H3))) |
-(csubt_abst c0 c3 H2 u0 t H3) \Rightarrow (\lambda (H4: (eq C (CHead c0 (Bind
-Abst) t) (CHead d1 (Flat f) u))).(\lambda (H5: (eq C (CHead c3 (Bind Abbr)
-u0) c2)).((let H6 \def (eq_ind C (CHead c0 (Bind Abst) t) (\lambda (e:
-C).(match e in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow
-False | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop)
-with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1
-(Flat f) u) H4) in (False_ind ((eq C (CHead c3 (Bind Abbr) u0) c2) \to
-((csubt g c0 c3) \to ((ty3 g c3 u0 t) \to (ex2 C (\lambda (d2: C).(csubt g d1
-d2)) (\lambda (d2: C).(drop O O c2 (CHead d2 (Flat f) u))))))) H6)) H5 H2
-H3)))]) in (H2 (refl_equal C (CHead d1 (Flat f) u)) (refl_equal C
-c2)))))))))) (\lambda (n0: nat).(\lambda (H: ((\forall (c1: C).(\forall (c2:
-C).((csubt g c1 c2) \to (\forall (d1: C).(\forall (u: T).((drop n0 O c1
-(CHead d1 (Flat f) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda
-(d2: C).(drop n0 O c2 (CHead d2 (Flat f) u)))))))))))).(\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 (u: T).((drop (S n0) O c (CHead
-d1 (Flat f) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
-C).(drop (S n0) O c0 (CHead d2 (Flat f) u))))))))) (\lambda (n1:
-nat).(\lambda (d1: C).(\lambda (u: T).(\lambda (H1: (drop (S n0) O (CSort n1)
-(CHead d1 (Flat f) u))).(let H2 \def (match H1 in drop return (\lambda (n2:
-nat).(\lambda (n3: nat).(\lambda (c: C).(\lambda (c0: C).(\lambda (_: (drop
-n2 n3 c c0)).((eq nat n2 (S n0)) \to ((eq nat n3 O) \to ((eq C c (CSort n1))
-\to ((eq C c0 (CHead d1 (Flat f) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1
-d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) (CHead d2 (Flat f)
-u))))))))))))) with [(drop_refl c) \Rightarrow (\lambda (H2: (eq nat O (S
-n0))).(\lambda (H3: (eq nat O O)).(\lambda (H4: (eq C c (CSort n1))).(\lambda
-(H5: (eq C c (CHead d1 (Flat f) u))).((let H6 \def (eq_ind nat O (\lambda (e:
-nat).(match e in nat return (\lambda (_: nat).Prop) with [O \Rightarrow True
-| (S _) \Rightarrow False])) I (S n0) H2) in (False_ind ((eq nat O O) \to
-((eq C c (CSort n1)) \to ((eq C c (CHead d1 (Flat f) u)) \to (ex2 C (\lambda
-(d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) (CHead d2
-(Flat f) u))))))) H6)) H3 H4 H5))))) | (drop_drop k h c e H2 u0) \Rightarrow
-(\lambda (H3: (eq nat (S h) (S n0))).(\lambda (H4: (eq nat O O)).(\lambda
-(H5: (eq C (CHead c k u0) (CSort n1))).(\lambda (H6: (eq C e (CHead d1 (Flat
-f) u))).((let H7 \def (f_equal nat nat (\lambda (e0: nat).(match e0 in nat
-return (\lambda (_: nat).nat) with [O \Rightarrow h | (S n2) \Rightarrow
-n2])) (S h) (S n0) H3) in (eq_ind nat n0 (\lambda (n2: nat).((eq nat O O) \to
-((eq C (CHead c k u0) (CSort n1)) \to ((eq C e (CHead d1 (Flat f) u)) \to
-((drop (r k n2) O c e) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda
-(d2: C).(drop (S n0) O (CSort n1) (CHead d2 (Flat f) u))))))))) (\lambda (_:
-(eq nat O O)).(\lambda (H9: (eq C (CHead c k u0) (CSort n1))).(let H10 \def
-(eq_ind C (CHead c k u0) (\lambda (e0: C).(match e0 in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ _ _) \Rightarrow
-True])) I (CSort n1) H9) in (False_ind ((eq C e (CHead d1 (Flat f) u)) \to
-((drop (r k n0) O c e) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda
-(d2: C).(drop (S n0) O (CSort n1) (CHead d2 (Flat f) u)))))) H10)))) h
-(sym_eq nat h n0 H7))) H4 H5 H6 H2))))) | (drop_skip k h d c e H2 u0)
-\Rightarrow (\lambda (H3: (eq nat h (S n0))).(\lambda (H4: (eq nat (S d)
-O)).(\lambda (H5: (eq C (CHead c k (lift h (r k d) u0)) (CSort n1))).(\lambda
-(H6: (eq C (CHead e k u0) (CHead d1 (Flat f) u))).(eq_ind nat (S n0) (\lambda
-(n2: nat).((eq nat (S d) O) \to ((eq C (CHead c k (lift n2 (r k d) u0))
-(CSort n1)) \to ((eq C (CHead e k u0) (CHead d1 (Flat f) u)) \to ((drop n2 (r
-k d) c e) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop
-(S n0) O (CSort n1) (CHead d2 (Flat f) u))))))))) (\lambda (H7: (eq nat (S d)
-O)).(let H8 \def (eq_ind nat (S d) (\lambda (e0: nat).(match e0 in nat return
-(\lambda (_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow True]))
-I O H7) in (False_ind ((eq C (CHead c k (lift (S n0) (r k d) u0)) (CSort n1))
-\to ((eq C (CHead e k u0) (CHead d1 (Flat f) u)) \to ((drop (S n0) (r k d) c
-e) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0)
-O (CSort n1) (CHead d2 (Flat f) u))))))) H8))) h (sym_eq nat h (S n0) H3) H4
-H5 H6 H2)))))]) in (H2 (refl_equal nat (S n0)) (refl_equal nat O) (refl_equal
-C (CSort n1)) (refl_equal C (CHead d1 (Flat f) u)))))))) (\lambda (c0:
-C).(\lambda (c3: C).(\lambda (H1: (csubt g c0 c3)).(\lambda (H2: ((\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 (k: K).(K_ind (\lambda (k0: K).(\forall (u:
-T).(\forall (d1: C).(\forall (u0: T).((drop (S n0) O (CHead c0 k0 u) (CHead
-d1 (Flat f) u0)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
-C).(drop (S n0) O (CHead c3 k0 u) (CHead d2 (Flat f) u0))))))))) (\lambda (b:
-B).(\lambda (u: T).(\lambda (d1: C).(\lambda (u0: T).(\lambda (H3: (drop (S
-n0) O (CHead c0 (Bind b) u) (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 b) u) (CHead d2 (Flat f) u0)))) (\lambda (x: C).(\lambda (H4:
-(csubt g d1 x)).(\lambda (H5: (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 b) u) (CHead d2 (Flat f) u0))) x H4 (drop_drop (Bind
-b) n0 c3 (CHead x (Flat f) u0) H5 u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop
-(Bind b) c0 (CHead d1 (Flat f) u0) u n0 H3)))))))) (\lambda (f0: F).(\lambda
+(CHead d1 (Flat f) u) (drop_gen_refl c1 (CHead d1 (Flat f) u) H0)) in (let
+H_x \def (csubt_gen_flat g d1 c2 u f H1) in (let H2 \def H_x in (ex2_ind C
+(\lambda (e2: C).(eq C c2 (CHead e2 (Flat f) u))) (\lambda (e2: C).(csubt g
+d1 e2)) (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop O O
+c2 (CHead d2 (Flat f) u)))) (\lambda (x: C).(\lambda (H3: (eq C c2 (CHead x
+(Flat f) u))).(\lambda (H4: (csubt g d1 x)).(eq_ind_r C (CHead x (Flat f) u)
+(\lambda (c: C).(ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2:
+C).(drop O O c (CHead d2 (Flat f) u))))) (ex_intro2 C (\lambda (d2: C).(csubt
+g d1 d2)) (\lambda (d2: C).(drop O O (CHead x (Flat f) u) (CHead d2 (Flat f)
+u))) x H4 (drop_refl (CHead x (Flat f) u))) c2 H3)))) H2)))))))))) (\lambda
+(n0: nat).(\lambda (H: ((\forall (c1: C).(\forall (c2: C).((csubt g c1 c2)
+\to (\forall (d1: C).(\forall (u: T).((drop n0 O c1 (CHead d1 (Flat f) u))
+\to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0 O c2
+(CHead d2 (Flat f) u)))))))))))).(\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 (u: T).((drop (S n0) O c (CHead d1 (Flat f) u)) \to (ex2 C
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O c0 (CHead
+d2 (Flat f) u))))))))) (\lambda (n1: nat).(\lambda (d1: C).(\lambda (u:
+T).(\lambda (H1: (drop (S n0) O (CSort n1) (CHead d1 (Flat f) u))).(and3_ind
+(eq C (CHead d1 (Flat f) u) (CSort n1)) (eq nat (S n0) O) (eq nat O O) (ex2 C
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1)
+(CHead d2 (Flat f) u)))) (\lambda (_: (eq C (CHead d1 (Flat f) u) (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 (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop
+(S n0) O (CSort n1) (CHead d2 (Flat f) u)))) H5))))) (drop_gen_sort n1 (S n0)
+O (CHead d1 (Flat f) u) H1)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda
+(H1: (csubt g c0 c3)).(\lambda (H2: ((\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 (k: K).(K_ind (\lambda (k0: K).(\forall (u: T).(\forall
+(d1: C).(\forall (u0: T).((drop (S n0) O (CHead c0 k0 u) (CHead d1 (Flat f)
+u0)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S
+n0) O (CHead c3 k0 u) (CHead d2 (Flat f) u0))))))))) (\lambda (b: B).(\lambda