1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 include "delayed_updating/unwind/unwind2_rmap_eq.ma".
16 include "delayed_updating/syntax/path_closed.ma".
17 include "delayed_updating/syntax/path_depth.ma".
18 include "ground/relocation/nap.ma".
19 include "ground/lib/stream_tls_plus.ma".
20 include "ground/lib/stream_eq_eq.ma".
22 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
24 (* Destructions with cpp ****************************************************)
26 lemma nap_plus_unwind2_rmap_closed (o) (f) (q) (m) (n):
28 f@§❨m❩+♭q = ▶[f]q@§❨m+n❩.
29 #o #f #q #m #n #Hq elim Hq -q -n //
30 #q #n [ #k #_ ] #_ #IH
31 [ <depth_d_dx <unwind2_rmap_d_dx
32 <tr_compose_nap <tr_uni_nap //
33 | <depth_L_dx <unwind2_rmap_L_dx
34 <tr_nap_push <nplus_succ_dx //
38 lemma nap_plus_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (m) (n):
40 (⫯▶[f]p)@§❨m❩+♭q = ▶[f](p●𝗟◗q)@§❨m+n❩.
42 /2 width=2 by nap_plus_unwind2_rmap_closed/
45 lemma nap_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
47 ♭q = ▶[f](p●𝗟◗q)@§❨n❩.
50 <(nap_plus_unwind2_rmap_append_closed_Lq_dx … Hn) -Hn
54 lemma tls_succ_plus_unwind2_rmap_push_closed (o) (f) (q) (n):
56 ∀m. ⇂*[m]f ≗ ⇂*[↑(m+n)]▶[⫯f]q.
57 #o #f #q #n #Hn elim Hn -q -n //
59 @(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
60 >nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold //
63 lemma tls_succ_unwind2_rmap_push_closed (o) (f) (q) (n):
67 /2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
70 lemma tls_succ_plus_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
72 ∀m. ⇂*[m]▶[f]p ≗ ⇂*[↑(m+n)]▶[f](p●𝗟◗q).
74 /2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/