--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "basic_1A/csubv/props.ma".
+
+include "basic_1A/csubv/fwd.ma".
+
+include "basic_1A/drop/fwd.ma".
+
+lemma csubv_drop_conf:
+ \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (e1:
+C).(\forall (h: nat).((drop h O c1 e1) \to (ex2 C (\lambda (e2: C).(csubv e1
+e2)) (\lambda (e2: C).(drop h O c2 e2))))))))
+\def
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubv c1 c2)).(csubv_ind
+(\lambda (c: C).(\lambda (c0: C).(\forall (e1: C).(\forall (h: nat).((drop h
+O c e1) \to (ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop h O
+c0 e2)))))))) (\lambda (n: nat).(\lambda (e1: C).(\lambda (h: nat).(\lambda
+(H0: (drop h O (CSort n) e1)).(and3_ind (eq C e1 (CSort n)) (eq nat h O) (eq
+nat O O) (ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop h O
+(CSort n) e2))) (\lambda (H1: (eq C e1 (CSort n))).(\lambda (H2: (eq nat h
+O)).(\lambda (_: (eq nat O O)).(eq_ind_r nat O (\lambda (n0: nat).(ex2 C
+(\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop n0 O (CSort n) e2))))
+(eq_ind_r C (CSort n) (\lambda (c: C).(ex2 C (\lambda (e2: C).(csubv c e2))
+(\lambda (e2: C).(drop O O (CSort n) e2)))) (ex_intro2 C (\lambda (e2:
+C).(csubv (CSort n) e2)) (\lambda (e2: C).(drop O O (CSort n) e2)) (CSort n)
+(csubv_refl (CSort n)) (drop_refl (CSort n))) e1 H1) h H2)))) (drop_gen_sort
+n h O e1 H0)))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csubv c3
+c4)).(\lambda (H1: ((\forall (e1: C).(\forall (h: nat).((drop h O c3 e1) \to
+(ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop h O c4
+e2)))))))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (e1: C).(\lambda (h:
+nat).(\lambda (H2: (drop h O (CHead c3 (Bind Void) v1) e1)).(nat_ind (\lambda
+(n: nat).((drop n O (CHead c3 (Bind Void) v1) e1) \to (ex2 C (\lambda (e2:
+C).(csubv e1 e2)) (\lambda (e2: C).(drop n O (CHead c4 (Bind Void) v2)
+e2))))) (\lambda (H3: (drop O O (CHead c3 (Bind Void) v1) e1)).(eq_ind C
+(CHead c3 (Bind Void) v1) (\lambda (c: C).(ex2 C (\lambda (e2: C).(csubv c
+e2)) (\lambda (e2: C).(drop O O (CHead c4 (Bind Void) v2) e2)))) (ex_intro2 C
+(\lambda (e2: C).(csubv (CHead c3 (Bind Void) v1) e2)) (\lambda (e2: C).(drop
+O O (CHead c4 (Bind Void) v2) e2)) (CHead c4 (Bind Void) v2) (csubv_bind_same
+c3 c4 H0 Void v1 v2) (drop_refl (CHead c4 (Bind Void) v2))) e1 (drop_gen_refl
+(CHead c3 (Bind Void) v1) e1 H3))) (\lambda (h0: nat).(\lambda (_: (((drop h0
+O (CHead c3 (Bind Void) v1) e1) \to (ex2 C (\lambda (e2: C).(csubv e1 e2))
+(\lambda (e2: C).(drop h0 O (CHead c4 (Bind Void) v2) e2)))))).(\lambda (H3:
+(drop (S h0) O (CHead c3 (Bind Void) v1) e1)).(let H_x \def (H1 e1 (r (Bind
+Void) h0) (drop_gen_drop (Bind Void) c3 e1 v1 h0 H3)) in (let H4 \def H_x in
+(ex2_ind C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop h0 O c4
+e2)) (ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop (S h0) O
+(CHead c4 (Bind Void) v2) e2))) (\lambda (x: C).(\lambda (H5: (csubv e1
+x)).(\lambda (H6: (drop h0 O c4 x)).(ex_intro2 C (\lambda (e2: C).(csubv e1
+e2)) (\lambda (e2: C).(drop (S h0) O (CHead c4 (Bind Void) v2) e2)) x H5
+(drop_drop (Bind Void) h0 c4 x H6 v2))))) H4)))))) h H2)))))))))) (\lambda
+(c3: C).(\lambda (c4: C).(\lambda (H0: (csubv c3 c4)).(\lambda (H1: ((\forall
+(e1: C).(\forall (h: nat).((drop h O c3 e1) \to (ex2 C (\lambda (e2:
+C).(csubv e1 e2)) (\lambda (e2: C).(drop h O c4 e2)))))))).(\lambda (b1:
+B).(\lambda (H2: (not (eq B b1 Void))).(\lambda (b2: B).(\lambda (v1:
+T).(\lambda (v2: T).(\lambda (e1: C).(\lambda (h: nat).(\lambda (H3: (drop h
+O (CHead c3 (Bind b1) v1) e1)).(nat_ind (\lambda (n: nat).((drop n O (CHead
+c3 (Bind b1) v1) e1) \to (ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2:
+C).(drop n O (CHead c4 (Bind b2) v2) e2))))) (\lambda (H4: (drop O O (CHead
+c3 (Bind b1) v1) e1)).(eq_ind C (CHead c3 (Bind b1) v1) (\lambda (c: C).(ex2
+C (\lambda (e2: C).(csubv c e2)) (\lambda (e2: C).(drop O O (CHead c4 (Bind
+b2) v2) e2)))) (ex_intro2 C (\lambda (e2: C).(csubv (CHead c3 (Bind b1) v1)
+e2)) (\lambda (e2: C).(drop O O (CHead c4 (Bind b2) v2) e2)) (CHead c4 (Bind
+b2) v2) (csubv_bind c3 c4 H0 b1 H2 b2 v1 v2) (drop_refl (CHead c4 (Bind b2)
+v2))) e1 (drop_gen_refl (CHead c3 (Bind b1) v1) e1 H4))) (\lambda (h0:
+nat).(\lambda (_: (((drop h0 O (CHead c3 (Bind b1) v1) e1) \to (ex2 C
+(\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop h0 O (CHead c4 (Bind
+b2) v2) e2)))))).(\lambda (H4: (drop (S h0) O (CHead c3 (Bind b1) v1)
+e1)).(let H_x \def (H1 e1 (r (Bind b1) h0) (drop_gen_drop (Bind b1) c3 e1 v1
+h0 H4)) in (let H5 \def H_x in (ex2_ind C (\lambda (e2: C).(csubv e1 e2))
+(\lambda (e2: C).(drop h0 O c4 e2)) (ex2 C (\lambda (e2: C).(csubv e1 e2))
+(\lambda (e2: C).(drop (S h0) O (CHead c4 (Bind b2) v2) e2))) (\lambda (x:
+C).(\lambda (H6: (csubv e1 x)).(\lambda (H7: (drop h0 O c4 x)).(ex_intro2 C
+(\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop (S h0) O (CHead c4
+(Bind b2) v2) e2)) x H6 (drop_drop (Bind b2) h0 c4 x H7 v2))))) H5)))))) h
+H3))))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csubv c3
+c4)).(\lambda (H1: ((\forall (e1: C).(\forall (h: nat).((drop h O c3 e1) \to
+(ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop h O c4
+e2)))))))).(\lambda (f1: F).(\lambda (f2: F).(\lambda (v1: T).(\lambda (v2:
+T).(\lambda (e1: C).(\lambda (h: nat).(\lambda (H2: (drop h O (CHead c3 (Flat
+f1) v1) e1)).(nat_ind (\lambda (n: nat).((drop n O (CHead c3 (Flat f1) v1)
+e1) \to (ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop n O
+(CHead c4 (Flat f2) v2) e2))))) (\lambda (H3: (drop O O (CHead c3 (Flat f1)
+v1) e1)).(eq_ind C (CHead c3 (Flat f1) v1) (\lambda (c: C).(ex2 C (\lambda
+(e2: C).(csubv c e2)) (\lambda (e2: C).(drop O O (CHead c4 (Flat f2) v2)
+e2)))) (ex_intro2 C (\lambda (e2: C).(csubv (CHead c3 (Flat f1) v1) e2))
+(\lambda (e2: C).(drop O O (CHead c4 (Flat f2) v2) e2)) (CHead c4 (Flat f2)
+v2) (csubv_flat c3 c4 H0 f1 f2 v1 v2) (drop_refl (CHead c4 (Flat f2) v2))) e1
+(drop_gen_refl (CHead c3 (Flat f1) v1) e1 H3))) (\lambda (h0: nat).(\lambda
+(_: (((drop h0 O (CHead c3 (Flat f1) v1) e1) \to (ex2 C (\lambda (e2:
+C).(csubv e1 e2)) (\lambda (e2: C).(drop h0 O (CHead c4 (Flat f2) v2)
+e2)))))).(\lambda (H3: (drop (S h0) O (CHead c3 (Flat f1) v1) e1)).(let H_x
+\def (H1 e1 (r (Flat f1) h0) (drop_gen_drop (Flat f1) c3 e1 v1 h0 H3)) in
+(let H4 \def H_x in (ex2_ind C (\lambda (e2: C).(csubv e1 e2)) (\lambda (e2:
+C).(drop (S h0) O c4 e2)) (ex2 C (\lambda (e2: C).(csubv e1 e2)) (\lambda
+(e2: C).(drop (S h0) O (CHead c4 (Flat f2) v2) e2))) (\lambda (x: C).(\lambda
+(H5: (csubv e1 x)).(\lambda (H6: (drop (S h0) O c4 x)).(ex_intro2 C (\lambda
+(e2: C).(csubv e1 e2)) (\lambda (e2: C).(drop (S h0) O (CHead c4 (Flat f2)
+v2) e2)) x H5 (drop_drop (Flat f2) h0 c4 x H6 v2))))) H4)))))) h
+H2)))))))))))) c1 c2 H))).
+