-(\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
-u2) (CHead e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
-(\lambda (_: C).(\lambda (u4: T).(pr0 u3 u4))))))))) \to (\forall (e1:
-C).(\forall (u3: T).(\forall (k1: K).((drop (S n) O (CHead c3 k0 u1) (CHead
-e1 k1 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(drop (S n) O
-(CHead c4 k0 u2) (CHead e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0
-e1 e2))) (\lambda (_: C).(\lambda (u4: T).(pr0 u3 u4))))))))))) (\lambda (b:
-B).(\lambda (n: nat).(\lambda (_: ((\forall (e1: C).(\forall (u3: T).(\forall
-(k0: K).((drop n O (CHead c3 (Bind b) u1) (CHead e1 k0 u3)) \to (ex3_2 C T
-(\lambda (e2: C).(\lambda (u4: T).(drop n O (CHead c4 (Bind b) u2) (CHead e2
-k0 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
-C).(\lambda (u4: T).(pr0 u3 u4)))))))))).(\lambda (e1: C).(\lambda (u0:
-T).(\lambda (k0: K).(\lambda (H4: (drop (S n) O (CHead c3 (Bind b) u1) (CHead
-e1 k0 u0))).(let H5 \def (H1 n e1 u0 k0 (drop_gen_drop (Bind b) c3 (CHead e1
-k0 u0) u1 n H4)) in (ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(drop n
-O c4 (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
-(\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))) (ex3_2 C T (\lambda (e2:
+((let H5 \def (f_equal C K (\lambda (e: C).(match e 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 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 u2) (CHead e2 k1 u4)))) (\lambda
+(e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u4: T).(pr0
+u3 u4))))))))) \to (\forall (e1: C).(\forall (u3: T).(\forall (k1: K).((drop
+(S n) O (CHead c3 k0 u1) (CHead e1 k1 u3)) \to (ex3_2 C T (\lambda (e2:
+C).(\lambda (u4: T).(drop (S n) O (CHead c4 k0 u2) (CHead e2 k1 u4))))
+(\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda
+(u4: T).(pr0 u3 u4))))))))))) (\lambda (b: B).(\lambda (n: nat).(\lambda (_:
+((\forall (e1: C).(\forall (u3: T).(\forall (k0: K).((drop n O (CHead c3
+(Bind b) u1) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4:
+T).(drop n O (CHead c4 (Bind b) u2) (CHead e2 k0 u4)))) (\lambda (e2:
+C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u4: T).(pr0 u3
+u4)))))))))).(\lambda (e1: C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H4:
+(drop (S n) O (CHead c3 (Bind b) u1) (CHead e1 k0 u0))).(let H5 \def (H1 n e1
+u0 k0 (drop_gen_drop (Bind b) c3 (CHead e1 k0 u0) u1 n H4)) in (ex3_2_ind C T
+(\lambda (e2: C).(\lambda (u3: T).(drop n O c4 (CHead e2 k0 u3)))) (\lambda
+(e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0
+u0 u3))) (ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(drop (S n) O (CHead c4
+(Bind b) u2) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1
+e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3)))) (\lambda (x0:
+C).(\lambda (x1: T).(\lambda (H6: (drop n O c4 (CHead x0 k0 x1))).(\lambda
+(H7: (wcpr0 e1 x0)).(\lambda (H8: (pr0 u0 x1)).(ex3_2_intro C T (\lambda (e2: