-theorem ifr_unwind_bi (f) (p) (q) (t1) (t2):
- t1 Ο΅ π β t1β(pβπ¦) β§Έβ¬ π β
- t1 β‘π[p,q] t2 β βΌ[f]t1 β‘π[βp,βq] βΌ[f]t2.
-#f #p #q #t1 #t2 #H1t1 #H2t1
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro β¦ (ββq)) @and3_intro
-[ -H1t1 -H2t1 -Ht1 -Ht2
- >structure_L_sn >structure_reverse
- >H1n >path_head_structure_depth <H1n -H1n //
-| lapply (in_comp_unwind2_path_term f β¦ Ht1) -Ht2 -Ht1 -H1t1 -H2t1
- <unwind2_path_d_dx
- >list_append_rcons_sn in H1n; <reverse_append #H1n
- lapply (unwind2_rmap_append_pap_closed f β¦ H1n)
- <reverse_lcons <depth_L_dx #H2n
- lapply (eq_inv_ninj_bi β¦ H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
+lemma ifr_unwind_bi (f) (t1) (t2) (r):
+ t1 Ο΅ π β r Ο΅ π β
+ t1 β‘π’π[r] t2 β βΌ[f]t1 β‘π’π[βr] βΌ[f]t2.
+#f #t1 #t2 #r #H1t1 #H2r
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro β¦ (βp) (βq) (βq))
+[ -H1t1 -H2r -Hn -Ht1 -Ht2 //
+| -H1t1 -H2r -Ht1 -Ht2
+ /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term f β¦ Ht1) -Ht2 -Ht1 -H1t1 -H2r
+ <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn
+ <nap_unwind2_rmap_append_closed_Lq_dx_depth //