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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "delayed_updating/substitution/lift_path.ma".
16 include "delayed_updating/syntax/path_closed.ma".
17 include "ground/relocation/xap.ma".
19 (* LIFT FOR PATH ************************************************************)
21 (* Constructions with pcc ***************************************************)
23 lemma lift_path_closed (o) (f) (q) (n):
24 q ϵ 𝐂❨o,n❩ → 🠡[f]q ϵ 𝐂❨o,🠢[f]q@❨n❩❩.
25 #o #f #q #n #H0 elim H0 -q -n //
26 #q #n [ #k #Ho ] #_ #IH
27 /2 width=1 by pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
28 /4 width=1 by pcc_d_dx, tr_xap_pos/
31 lemma lift_path_rmap_closed (o) (f) (p) (q) (n):
32 q ϵ 𝐂❨o,n❩ → 🠡[🠢[f]p]q ϵ 𝐂❨o,🠢[f](p●q)@❨n❩❩.
33 /2 width=1 by lift_path_closed/
36 lemma lift_path_rmap_closed_L (o) (f) (p) (q) (n):
37 q ϵ 𝐂❨o,n❩ → 🠡[🠢[f](p◖𝗟)]q ϵ 𝐂❨o,🠢[f](p●𝗟◗q)@§❨n❩❩.
39 lapply (lift_path_closed … (🠢[f](p◖𝗟)) … Hq) #Hq0
40 lapply (pcc_L_sn … Hq) -Hq #Hq1
41 lapply (lift_path_rmap_closed … f p … Hq1) -Hq1
42 <lift_path_L_sn >lift_rmap_L_dx #Hq1
43 elim (pcc_inv_L_sn … Hq1 Hq0) -Hq1 #H0 #_