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4 (* ||A|| A project by Andrea Asperti *)
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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 (f) (q) (n):
24 q ϵ 𝐂❨n❩ → ↑[f]q ϵ 𝐂❨↑[q]f@❨n❩❩.
25 #f #q #n #Hq elim Hq -Hq //
27 /2 width=1 by pcc_d_dx, pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
30 lemma lift_path_rmap_closed (f) (p) (q) (n):
31 q ϵ 𝐂❨n❩ → ↑[↑[p]f]q ϵ 𝐂❨↑[p●q]f@❨n❩❩.
32 /2 width=1 by lift_path_closed/