--- /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/getl/fwd.ma".
+
+include "basic_1A/clear/props.ma".
+
+include "basic_1A/drop/props.ma".
+
+lemma getl_refl:
+ \forall (b: B).(\forall (c: C).(\forall (u: T).(getl O (CHead c (Bind b) u)
+(CHead c (Bind b) u))))
+\def
+ \lambda (b: B).(\lambda (c: C).(\lambda (u: T).(getl_intro O (CHead c (Bind
+b) u) (CHead c (Bind b) u) (CHead c (Bind b) u) (drop_refl (CHead c (Bind b)
+u)) (clear_bind b c u)))).
+
+lemma getl_head:
+ \forall (k: K).(\forall (h: nat).(\forall (c: C).(\forall (e: C).((getl (r k
+h) c e) \to (\forall (u: T).(getl (S h) (CHead c k u) e))))))
+\def
+ \lambda (k: K).(\lambda (h: nat).(\lambda (c: C).(\lambda (e: C).(\lambda
+(H: (getl (r k h) c e)).(\lambda (u: T).(let H0 \def (getl_gen_all c e (r k
+h) H) in (ex2_ind C (\lambda (e0: C).(drop (r k h) O c e0)) (\lambda (e0:
+C).(clear e0 e)) (getl (S h) (CHead c k u) e) (\lambda (x: C).(\lambda (H1:
+(drop (r k h) O c x)).(\lambda (H2: (clear x e)).(getl_intro (S h) (CHead c k
+u) e x (drop_drop k h c x H1 u) H2)))) H0))))))).
+
+lemma getl_flat:
+ \forall (c: C).(\forall (e: C).(\forall (h: nat).((getl h c e) \to (\forall
+(f: F).(\forall (u: T).(getl h (CHead c (Flat f) u) e))))))
+\def
+ \lambda (c: C).(\lambda (e: C).(\lambda (h: nat).(\lambda (H: (getl h c
+e)).(\lambda (f: F).(\lambda (u: T).(let H0 \def (getl_gen_all c e h H) in
+(ex2_ind C (\lambda (e0: C).(drop h O c e0)) (\lambda (e0: C).(clear e0 e))
+(getl h (CHead c (Flat f) u) e) (\lambda (x: C).(\lambda (H1: (drop h O c
+x)).(\lambda (H2: (clear x e)).(nat_ind (\lambda (n: nat).((drop n O c x) \to
+(getl n (CHead c (Flat f) u) e))) (\lambda (H3: (drop O O c x)).(let H4 \def
+(eq_ind_r C x (\lambda (c0: C).(clear c0 e)) H2 c (drop_gen_refl c x H3)) in
+(getl_intro O (CHead c (Flat f) u) e (CHead c (Flat f) u) (drop_refl (CHead c
+(Flat f) u)) (clear_flat c e H4 f u)))) (\lambda (h0: nat).(\lambda (_:
+(((drop h0 O c x) \to (getl h0 (CHead c (Flat f) u) e)))).(\lambda (H3: (drop
+(S h0) O c x)).(getl_intro (S h0) (CHead c (Flat f) u) e x (drop_drop (Flat
+f) h0 c x H3 u) H2)))) h H1)))) H0))))))).
+
+lemma getl_ctail:
+ \forall (b: B).(\forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i:
+nat).((getl i c (CHead d (Bind b) u)) \to (\forall (k: K).(\forall (v:
+T).(getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)))))))))
+\def
+ \lambda (b: B).(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
+nat).(\lambda (H: (getl i c (CHead d (Bind b) u))).(\lambda (k: K).(\lambda
+(v: T).(let H0 \def (getl_gen_all c (CHead d (Bind b) u) i H) in (ex2_ind C
+(\lambda (e: C).(drop i O c e)) (\lambda (e: C).(clear e (CHead d (Bind b)
+u))) (getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)) (\lambda (x:
+C).(\lambda (H1: (drop i O c x)).(\lambda (H2: (clear x (CHead d (Bind b)
+u))).(getl_intro i (CTail k v c) (CHead (CTail k v d) (Bind b) u) (CTail k v
+x) (drop_ctail c x O i H1 k v) (clear_ctail b x d u H2 k v))))) H0))))))))).
+