(* Constructions with pcc ***************************************************)
lemma lift_path_closed (o) (f) (q) (n):
- q ϵ 𝐂❨o,n❩ → ↑[f]q ϵ 𝐂❨o,↑[q]f@❨n❩❩.
+ q ϵ 𝐂❨o,n❩ → 🠡[f]q ϵ 𝐂❨o,🠢[f]q@❨n❩❩.
#o #f #q #n #H0 elim H0 -q -n //
#q #n [ #k #Ho ] #_ #IH
/2 width=1 by pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
qed.
lemma lift_path_rmap_closed (o) (f) (p) (q) (n):
- q ϵ 𝐂❨o,n❩ → ↑[↑[p]f]q ϵ 𝐂❨o,↑[p●q]f@❨n❩❩.
+ q ϵ 𝐂❨o,n❩ → 🠡[🠢[f]p]q ϵ 𝐂❨o,🠢[f](p●q)@❨n❩❩.
/2 width=1 by lift_path_closed/
qed.
lemma lift_path_rmap_closed_L (o) (f) (p) (q) (n):
- q ϵ 𝐂❨o,n❩ → ↑[↑[p◖𝗟]f]q ϵ 𝐂❨o,↑[p●𝗟◗q]f@§❨n❩❩.
+ q ϵ 𝐂❨o,n❩ → 🠡[🠢[f](p◖𝗟)]q ϵ 𝐂❨o,🠢[f](p●𝗟◗q)@§❨n❩❩.
#o #f #p #q #n #Hq
-lapply (lift_path_closed … (↑[p◖𝗟]f) … Hq) #Hq0
+lapply (lift_path_closed … (🠢[f](p◖𝗟)) … Hq) #Hq0
lapply (pcc_L_sn … Hq) -Hq #Hq1
lapply (lift_path_rmap_closed … f p … Hq1) -Hq1
<lift_path_L_sn >lift_rmap_L_dx #Hq1