include "delayed_updating/unwind/unwind2_constructors.ma".
include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
include "delayed_updating/unwind/unwind2_preterm_eq.ma".
-include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
include "delayed_updating/unwind/unwind2_rmap_head.ma".
include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
include "delayed_updating/syntax/prototerm_proper_constructors.ma".
include "delayed_updating/syntax/path_head_structure.ma".
(* 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
-[ -H0t1 -H1n -Ht1 -Ht2
- >list_append_rcons_sn <reverse_append
- >nsucc_unfold >depth_reverse >depth_L_dx >reverse_lcons
+@(ex_intro … (↑♭q)) @and3_intro
+[ -H0t1 -Ht1 -Ht2
>structure_L_sn >structure_reverse
- <path_head_structure //
+ >H1n >path_head_structure_depth <H1n -H1n //
| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
- <unwind2_path_d_dx <depth_structure
+ <unwind2_path_d_dx
>list_append_rcons_sn in H1n; <reverse_append #H1n
lapply (unwind2_rmap_append_pap_closed f … H1n)
<reverse_lcons <depth_L_dx #H2n
@(subset_eq_trans … (unwind2_term_fsubst …))
[ @fsubst_eq_repl [ // | // ]
@(subset_eq_trans … (unwind2_term_iref …))
- @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+ @(subset_eq_canc_sn … (unwind2_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 … (unwind2_term_after …))
@unwind2_term_eq_repl_sn
(* Note: crux of the proof begins *)
@nstream_eq_inv_ext #m
>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 //
+ lapply (tls_unwind2_rmap_append_closed f … H1n) -H1n #H2n
+ <(tr_pap_eq_repl … H2n) -H2n //
(* Note: crux of the proof ends *)
| //
| /2 width=2 by ex_intro/