(* Main destructions with ifr ***********************************************)
theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
- t1 ➡𝐝𝐟[p,q] t2 → ▼[f]t1 ➡𝐟[⊗p,⊗q] ▼[f]t2.
+ t1 â\9e¡ð\9d\90\9dð\9d\90\9f[p,q] t2 â\86\92 â\96¼[f]t1 â\9e¡ð\9d\90¢ð\9d\90\9f[â\8a\97p,â\8a\97q] â\96¼[f]t2.
#f #p #q #t1 #t2 #H0t1
* #n * #H1n #Ht1 #Ht2
-@(ex_intro … (↑♭⊗q)) @and3_intro
+@(ex_intro … (↑♭q)) @and3_intro
[ -H0t1 -Ht1 -Ht2
>structure_L_sn >structure_reverse
- >H1n >path_head_structure_depth <H1n -H1n //
+ >H1n in ⊢ (??%?); >path_head_structure_depth <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)
+ <unwind2_path_d_dx >(list_append_rcons_sn … p) <reverse_append
+ lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔)ᴿ … H1n) -H1n
<reverse_lcons <depth_L_dx #H2n
- lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
+ lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n #Ht1 //
| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
@(subset_eq_trans … Ht2) -t2
@(subset_eq_trans … (unwind2_term_fsubst …))
@(subset_eq_trans … (unwind2_term_iref …))
@(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
[ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
- @(subset_eq_trans … (unwind2_lift_term_after …))
+ @(subset_eq_trans … (lift_unwind2_term_after …))
@unwind2_term_eq_repl_sn
(* Note: crux of the proof begins *)
- @nstream_eq_inv_ext #m
- <tr_compose_pap <tr_compose_pap
- <tr_uni_pap <tr_uni_pap <tr_pap_plus
- >list_append_rcons_sn in H1n; <reverse_append #H1n
- lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
- >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
- lapply (tls_unwind2_rmap_append_closed f … H1n) #H2n
- <(tr_pap_eq_repl … H2n) -H2n -H1n //
+ >list_append_rcons_sn <reverse_append
+ @(stream_eq_trans … (tr_compose_uni_dx …))
+ @tr_compose_eq_repl
+ [ <unwind2_rmap_append_pap_closed //
+ | >unwind2_rmap_A_sn <reverse_rcons
+ /2 width=1 by tls_unwind2_rmap_closed/
+ ]
(* Note: crux of the proof ends *)
| //
| /2 width=2 by ex_intro/