-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.
-#f #p #q #t1 #t2
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)@⧣❨n❩)) @and3_intro
-[ -Ht1 -Ht2
- <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
- lapply (unwind2_rmap_append_pap_closed f … H1n)
- <reverse_lcons <depth_L_dx #H2n
- lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
-| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
+theorem dfr_lift_bi (f) (t1) (t2) (r):
+ t1 ➡𝐝𝐟[r] t2 → 🠡[f]t1 ➡𝐝𝐟[🠡[f]r] 🠡[f]t2.
+#f #t1 #t2 #r
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔◖𝗟)]q) (🠢[f](p●𝗔◗𝗟◗q)@§❨n❩))
+[ -Hn -Ht1 -Ht2 //
+| -Ht1 -Ht2
+ /2 width=1 by lift_path_rmap_closed_L/
+| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -Hn
+ <lift_path_d_dx #Ht1 //
+| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1