*)
include "delayed_updating/substitution/fsubst_eq.ma".
include "delayed_updating/substitution/lift_prototerm_eq.ma".
+include "delayed_updating/substitution/lift_path_head.ma".
include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+
(* DELAYED FOCUSED REDUCTION ************************************************)
(* Constructions with lift **************************************************)
+(*
+lemma pippo (f) (r):
+ ↑[↑[r]f](rᴿ) = (↑[f]r)ᴿ.
+#f #r @(list_ind_rcons … r) -r //
+#p * [ #n ] #IH
+[ <reverse_rcons <lift_path_d_sn <lift_rmap_d_dx
+ <lift_path_d_dx <reverse_rcons
+ <IH
+*)
theorem dfr_lift_bi (f) (p) (q) (t1) (t2): (*t1 ϵ 𝐓 → *)
t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
* #n * #H1n #Ht1 #Ht2
@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)@⧣❨n❩)) @and3_intro
[ -Ht1 -Ht2
- >H1n >path_head_structure_depth <H1n -H1n //
+ <lift_rmap_L_dx >lift_path_L_sn
+ >list_append_rcons_sn in H1n; <reverse_append #H1n
+ <(lift_path_head … H1n) -H1n //
+(*
| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
<unwind2_path_d_dx <depth_structure
>list_append_rcons_sn in H1n; <reverse_append #H1n
]
]
qed.
+*)
\ No newline at end of file