-theorem ifr_unwind_bi (f) (p) (q) (t1) (t2):
- t1 Ļµ š ā t1ā(pāš¦) Ļµ š ā
- t1 ā”š[p,q] t2 ā ā¼[f]t1 ā”š[āp,āq] ā¼[f]t2.
-#f #p #q #t1 #t2 #H1t1 #H2t1
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro ā¦ (āāāq)) @and3_intro
-[ -H0t1 -Ht1 -Ht2
- >structure_L_sn >structure_reverse
- >H1n >path_head_structure_depth <H1n -H1n //
-| lapply (in_comp_unwind2_path_term f ā¦ 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 ā¦ H1n)
- <reverse_lcons <depth_L_dx #H2n
- lapply (eq_inv_ninj_bi ā¦ H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
+lemma ifr_unwind_bi (f) (t1) (t2) (r):
+ t1 Ļµ š ā r Ļµ š ā
+ t1 ā”š¢š[r] t2 ā ā¼[f]t1 ā”š¢š[ār] ā¼[f]t2.
+#f #t1 #t2 #r #H1t1 #H2r
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro ā¦ (āp) (āq) (āq))
+[ -H1t1 -H2r -Hn -Ht1 -Ht2 //
+| -H1t1 -H2r -Ht1 -Ht2
+ /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H1t1 -H2r
+ <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn
+ <unwind2_rmap_append_closed_Lq_dx_nap_depth //