(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_gen_eq.ma".
include "delayed_updating/syntax/path_head.ma".
include "delayed_updating/syntax/path_reverse.ma".
include "ground/relocation/xap.ma".
(* Constructions with head for path *****************************************)
lemma lift_path_head (f) (p) (q) (n):
- pᴿ = ↳[n](pᴿ●qᴿ) →
- ↳[↑[q●p]f@❨n❩](↑[f](q●p))ᴿ = (↑[↑[q]f]p)ᴿ.
+ pᴿ = ↳[n](pᴿ) →
+ ↳[↑[q●p]f@❨n❩](↑[↑[q]f]p)ᴿ = (↑[↑[q]f]p)ᴿ.
#f #p @(list_ind_rcons … p) -p
[ #q #n #H0
<(eq_inv_path_empty_head … H0) -H0
[ <reverse_rcons <path_head_d_sn #H0
elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
<list_append_assoc <lift_rmap_d_dx <lift_path_d_dx <reverse_rcons
- <tr_xap_succ_nap <path_head_d_sn >tr_xap_succ_nap
- <lift_path_d_dx >lift_rmap_append <reverse_rcons
- <(IH … H0) -IH -H0 <tr_xap_plus //
+ <tr_xap_succ_nap <path_head_d_sn
+ <(IH … H0) in ⊢ (???%); -IH -H0 <tr_xap_plus //
| <reverse_rcons <path_head_m_sn #H0
elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
<list_append_assoc <lift_rmap_m_dx <lift_path_m_dx <reverse_rcons
- <tr_xap_succ_nap <path_head_m_sn >tr_xap_succ_nap
- <lift_path_m_dx <reverse_rcons
- <(IH … H0) -IH -H0 //
+ <tr_xap_succ_nap <path_head_m_sn
+ <(IH … H0) in ⊢ (???%); -IH -H0 //
| <reverse_rcons <path_head_L_sn #H0
elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
<list_append_assoc <lift_rmap_L_dx <lift_path_L_dx <reverse_rcons
- <tr_xap_succ_nap <path_head_L_sn >tr_xap_succ_nap
- <lift_path_L_dx <reverse_rcons
- <(IH … H0) -IH -H0 //
+ <tr_xap_succ_nap <path_head_L_sn
+ <(IH … H0) in ⊢ (???%); -IH -H0 //
| <reverse_rcons <path_head_A_sn #H0
elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
<list_append_assoc <lift_rmap_A_dx <lift_path_A_dx <reverse_rcons
- <tr_xap_succ_nap <path_head_A_sn >tr_xap_succ_nap
- <lift_path_A_dx <reverse_rcons
- <(IH … H0) -IH -H0 //
+ <tr_xap_succ_nap <path_head_A_sn
+ <(IH … H0) in ⊢ (???%); -IH -H0 //
| <reverse_rcons <path_head_S_sn #H0
elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
<list_append_assoc <lift_rmap_S_dx <lift_path_S_dx <reverse_rcons
- <tr_xap_succ_nap <path_head_S_sn >tr_xap_succ_nap
- <lift_path_S_dx <reverse_rcons
- <(IH … H0) -IH -H0 //
+ <tr_xap_succ_nap <path_head_S_sn
+ <(IH … H0) in ⊢ (???%); -IH -H0 //
]
]
]