-C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H3: (drop O O (CHead c0 k u1)
-(CHead e1 k0 u0))).(let H4 \def (match (drop_gen_refl (CHead c0 k u1) (CHead
-e1 k0 u0) H3) in eq return (\lambda (c: C).(\lambda (_: (eq ? ? c)).((eq C c
-(CHead e1 k0 u0)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(drop O O
-(CHead c3 k u2) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0
-e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))))))) with [refl_equal
-\Rightarrow (\lambda (H4: (eq C (CHead c0 k u1) (CHead e1 k0 u0))).(let H5
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u1 | (CHead _ _ t) \Rightarrow t])) (CHead c0 k
-u1) (CHead e1 k0 u0) H4) in ((let H6 \def (f_equal C K (\lambda (e: C).(match
-e in C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k1
-_) \Rightarrow k1])) (CHead c0 k u1) (CHead e1 k0 u0) H4) 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 u1)
-(CHead e1 k0 u0) H4) in (eq_ind C e1 (\lambda (_: C).((eq K k k0) \to ((eq T
-u1 u0) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(drop O O (CHead c3 k
-u2) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
-(\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))))))) (\lambda (H8: (eq K k
-k0)).(eq_ind K k0 (\lambda (k1: K).((eq T u1 u0) \to (ex3_2 C T (\lambda (e2:
-C).(\lambda (u3: T).(drop O O (CHead c3 k1 u2) (CHead e2 k0 u3)))) (\lambda
-(e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0
-u0 u3)))))) (\lambda (H9: (eq T u1 u0)).(eq_ind T u0 (\lambda (_: T).(ex3_2 C
-T (\lambda (e2: C).(\lambda (u3: T).(drop O O (CHead c3 k0 u2) (CHead e2 k0
-u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
-C).(\lambda (u3: T).(pr0 u0 u3))))) (let H10 \def (eq_ind T u1 (\lambda (t:
-T).(pr0 t u2)) H2 u0 H9) in (let H11 \def (eq_ind C c0 (\lambda (c: C).(wcpr0
-c c3)) H0 e1 H7) in (ex3_2_intro C T (\lambda (e2: C).(\lambda (u3: T).(drop
-O O (CHead c3 k0 u2) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_:
-T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))) c3 u2
-(drop_refl (CHead c3 k0 u2)) H11 H10))) u1 (sym_eq T u1 u0 H9))) k (sym_eq K
-k k0 H8))) c0 (sym_eq C c0 e1 H7))) H6)) H5)))]) in (H4 (refl_equal C (CHead
-e1 k0 u0)))))))) (K_ind (\lambda (k0: K).(\forall (n: nat).(((\forall (e1:
-C).(\forall (u3: T).(\forall (k1: K).((drop n O (CHead c0 k0 u1) (CHead e1 k1
-u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(drop n O (CHead c3 k0
+C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H3: (drop O O (CHead c3 k u1)
+(CHead e1 k0 u0))).(let H4 \def (f_equal C C (\lambda (e: C).(match e in C
+return (\lambda (_: C).C) with [(CSort _) \Rightarrow c3 | (CHead c _ _)
+\Rightarrow c])) (CHead c3 k u1) (CHead e1 k0 u0) (drop_gen_refl (CHead c3 k
+u1) (CHead e1 k0 u0) H3)) in ((let H5 \def (f_equal C K (\lambda (e:
+C).(match e in C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k |
+(CHead _ k1 _) \Rightarrow k1])) (CHead c3 k u1) (CHead e1 k0 u0)
+(drop_gen_refl (CHead c3 k u1) (CHead e1 k0 u0) H3)) in ((let H6 \def
+(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
+[(CSort _) \Rightarrow u1 | (CHead _ _ t) \Rightarrow t])) (CHead c3 k u1)
+(CHead e1 k0 u0) (drop_gen_refl (CHead c3 k u1) (CHead e1 k0 u0) H3)) in
+(\lambda (H7: (eq K k k0)).(\lambda (H8: (eq C c3 e1)).(eq_ind K k (\lambda
+(k1: K).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(drop O O (CHead c4 k
+u2) (CHead e2 k1 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
+(\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))))) (eq_ind T u1 (\lambda (t:
+T).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(drop O O (CHead c4 k u2)
+(CHead e2 k u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda
+(_: C).(\lambda (u3: T).(pr0 t u3))))) (eq_ind C c3 (\lambda (c: C).(ex3_2 C
+T (\lambda (e2: C).(\lambda (u3: T).(drop O O (CHead c4 k u2) (CHead e2 k
+u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 c e2))) (\lambda (_:
+C).(\lambda (u3: T).(pr0 u1 u3))))) (ex3_2_intro C T (\lambda (e2:
+C).(\lambda (u3: T).(drop O O (CHead c4 k u2) (CHead e2 k u3)))) (\lambda
+(e2: C).(\lambda (_: T).(wcpr0 c3 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0
+u1 u3))) c4 u2 (drop_refl (CHead c4 k u2)) H0 H2) e1 H8) u0 H6) k0 H7))))
+H5)) H4)))))) (K_ind (\lambda (k0: K).(\forall (n: nat).(((\forall (e1:
+C).(\forall (u3: T).(\forall (k1: K).((drop n O (CHead c3 k0 u1) (CHead e1 k1
+u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(drop n O (CHead c4 k0