include "delayed_updating/substitution/lift_structure_depth.ma".
include "delayed_updating/syntax/prototerm_proper_constructors.ma".
include "delayed_updating/syntax/path_structure_depth.ma".
+include "ground/relocation/tr_uni_compose.ma".
include "ground/relocation/tr_pap_pushs.ma".
+include "ground/lib/stream_eq_eq.ma".
+
(* DELAYED FOCUSED REDUCTION ************************************************)
lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
@(subset_eq_trans … Ht2) -t2
@(subset_eq_trans … (lift_fsubst …))
- [ <structure_append <structure_A_sn <structure_append <structure_L_sn
+ [ <lift_rmap_append <lift_rmap_A_sn <lift_rmap_append <lift_rmap_L_sn
+ <structure_append <structure_A_sn <structure_append <structure_L_sn
+ <depth_append <depth_L_sn <depth_structure <depth_structure
@fsubst_eq_repl [ // ]
@(subset_eq_trans … (lift_iref …))
@(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
@(subset_eq_trans … (lift_term_after …))
@(subset_eq_canc_dx … (lift_term_after …))
@lift_term_eq_repl_sn -t1
+ @(stream_eq_trans … (tr_compose_uni_dx …))
+(*
+ >nrplus_inj_dx <tr_pap_plus
+*)
| //
| /2 width=2 by ex_intro/
| //