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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "delayed_updating/substitution/lift_rmap_eq.ma".
16 include "delayed_updating/syntax/path_closed.ma".
17 include "ground/relocation/xap.ma".
18 include "ground/lib/stream_eq_eq.ma".
20 (* LIFT MAP FOR PATH ********************************************************)
22 (* Destructions with cpp ****************************************************)
24 lemma tls_plus_lift_rmap_closed (o) (f) (q) (n):
26 ∀m. ⇂*[m]f ≗ ⇂*[m+n]🠢[f]q.
27 #o #f #q #n #Hq elim Hq -q -n //
30 lemma tls_lift_rmap_closed (o) (f) (q) (n):
34 /2 width=2 by tls_plus_lift_rmap_closed/
37 lemma tls_lift_rmap_append_closed_dx (o) (f) (p) (q) (n):
39 🠢[f]p ≗ ⇂*[n]🠢[f](p●q).
41 /2 width=2 by tls_lift_rmap_closed/
44 lemma tls_succ_lift_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
46 🠢[f]p ≗ ⇂*[↑n]🠢[f](p●𝗟◗q).
48 /3 width=2 by tls_lift_rmap_append_closed_dx, pcc_L_sn/
51 lemma tls_succ_plus_lift_rmap_append_closed_bLq_dx (o1) (o2) (f) (p) (b) (q) (m) (n):
52 b ϵ 𝐂❨o1,m❩ → q ϵ 𝐂❨o2,n❩ →
53 🠢[f]p ≗ ⇂*[↑(m+n)]🠢[f](p●b●𝗟◗q).
54 #o1 #o2 #f #p #b #q #m #n #Hm #Hn
55 >nplus_succ_dx <stream_tls_plus
56 @(stream_eq_trans … (tls_lift_rmap_append_closed_dx … Hm))
57 /3 width=2 by stream_tls_eq_repl, tls_succ_lift_rmap_append_closed_Lq_dx/
60 lemma nap_plus_lift_rmap_append_closed_Lq_dx (o) (f) (p) (q) (m) (n):
62 🠢[f](p)@❨m❩+🠢[f](p●𝗟◗q)@§❨n❩ = 🠢[f](p●𝗟◗q)@§❨m+n❩.
64 /4 width=2 by eq_f2, tr_xap_eq_repl, tls_succ_lift_rmap_append_closed_Lq_dx/