include "delayed_updating/reduction/dfr.ma".
include "delayed_updating/reduction/ifr.ma".
include "delayed_updating/substitution/fsubst_lift.ma".
+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_pap_pushs.ma".
(* DELAYED FOCUSED REDUCTION ************************************************)
-lemma dfr_lift_bi (f) (p) (q) (t1) (t2): ÆŽt1 â
+lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 Ïĩ ð â
t1 âĄðð[p,q] t2 â â[f]t1 âĄð[âp,âq] â[f]t2.
-#f #p #q #t1 #t2 #Ht1
-* -t2 #b #Hr #Hb
+#f #p #q #t1 #t2 #H0t1
+* #b #n * #Hb #Hn #Ht1 #Ht2
+@(ex1_2_intro âĶ (âb) (ââqâ)) @and4_intro
+[ //
+| #g <lift_rmap_structure <depth_structure
+ >tr_pushs_swap <tr_pap_pushs_le //
+| lapply (in_comp_lift_bi f âĶ Ht1) -Ht1 -H0t1 -Hb -Ht2
+ <lift_d_empty_dx //
+| lapply (eq_lift_bi f âĶ Ht2) -Ht2 #Ht2
+ @(subset_eq_trans âĶ Ht2) -t2
+ @(subset_eq_trans âĶ (lift_fsubst âĶ))
+ [ <structure_append <structure_A_sn <structure_append <structure_L_sn
+ | //
+ | /2 width=2 by ex_intro/
+ | //
+ ]
+]