--- /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/flt/props.ma".
+
+lemma getl_flt:
+ \forall (b: B).(\forall (c: C).(\forall (e: C).(\forall (u: T).(\forall (i:
+nat).((getl i c (CHead e (Bind b) u)) \to (flt e u c (TLRef i)))))))
+\def
+ \lambda (b: B).(\lambda (c: C).(C_ind (\lambda (c0: C).(\forall (e:
+C).(\forall (u: T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to
+(flt e u c0 (TLRef i))))))) (\lambda (n: nat).(\lambda (e: C).(\lambda (u:
+T).(\lambda (i: nat).(\lambda (H: (getl i (CSort n) (CHead e (Bind b)
+u))).(getl_gen_sort n i (CHead e (Bind b) u) H (flt e u (CSort n) (TLRef
+i)))))))) (\lambda (c0: C).(\lambda (H: ((\forall (e: C).(\forall (u:
+T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to (flt e u c0 (TLRef
+i)))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e: C).(\lambda (u:
+T).(\lambda (i: nat).(nat_ind (\lambda (n: nat).((getl n (CHead c0 k t)
+(CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef n)))) (\lambda (H0:
+(getl O (CHead c0 k t) (CHead e (Bind b) u))).(K_ind (\lambda (k0: K).((clear
+(CHead c0 k0 t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k0 t) (TLRef
+O)))) (\lambda (b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e
+(Bind b) u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 with
+[(CSort _) \Rightarrow e | (CHead c1 _ _) \Rightarrow c1])) (CHead e (Bind b)
+u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1))
+in ((let H3 \def (f_equal C B (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b1)
+\Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e (Bind b) u) (CHead c0
+(Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in ((let H4
+\def (f_equal C T (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u |
+(CHead _ _ t0) \Rightarrow t0])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t)
+(clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in (\lambda (H5: (eq B b
+b0)).(\lambda (H6: (eq C e c0)).(eq_ind_r T t (\lambda (t0: T).(flt e t0
+(CHead c0 (Bind b0) t) (TLRef O))) (eq_ind_r C c0 (\lambda (c1: C).(flt c1 t
+(CHead c0 (Bind b0) t) (TLRef O))) (eq_ind B b (\lambda (b1: B).(flt c0 t
+(CHead c0 (Bind b1) t) (TLRef O))) (flt_arith0 (Bind b) c0 t O) b0 H5) e H6)
+u H4)))) H3)) H2)))) (\lambda (f: F).(\lambda (H1: (clear (CHead c0 (Flat f)
+t) (CHead e (Bind b) u))).(flt_arith1 (Bind b) e c0 u (clear_cle c0 (CHead e
+(Bind b) u) (clear_gen_flat f c0 (CHead e (Bind b) u) t H1)) (Flat f) t O)))
+k (getl_gen_O (CHead c0 k t) (CHead e (Bind b) u) H0))) (\lambda (n:
+nat).(\lambda (_: (((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (flt e u
+(CHead c0 k t) (TLRef n))))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead
+e (Bind b) u))).(let H_y \def (H e u (r k n) (getl_gen_S k c0 (CHead e (Bind
+b) u) t n H1)) in (flt_arith2 e c0 u (r k n) H_y k t (S n)))))) i)))))))) c)).
+