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/unwind1/unwind.ma".
16 include "delayed_updating/syntax/path_depth.ma".
17 include "ground/relocation/tr_id_compose.ma".
18 include "ground/relocation/tr_compose_compose.ma".
19 include "ground/relocation/tr_compose_pn.ma".
20 include "ground/relocation/tr_compose_eq.ma".
21 include "ground/relocation/tr_pn_eq.ma".
22 include "ground/lib/stream_eq_eq.ma".
24 (* UNWIND FOR PATH *********************************************************)
26 (* Constructions with depth ************************************************)
28 lemma unwind_rmap_decompose (p) (f):
29 ▼[p]f ≗ (▼[p]𝐢)∘(⫯*[❘p❘]f).
30 #p @(list_ind_rcons … p) -p
31 [ #f <unwind_rmap_empty <unwind_rmap_empty <tr_pushs_zero //
32 | #p * [ #n ] #IH #f //
33 [ <unwind_rmap_d_dx <unwind_rmap_d_dx <depth_d_dx
34 @(stream_eq_canc_dx … (tr_compose_assoc …))
35 /2 width=1 by tr_compose_eq_repl/
36 | <unwind_rmap_L_dx <unwind_rmap_L_dx <depth_L_dx
37 <tr_pushs_succ <tr_compose_push_bi
38 /2 width=1 by tr_push_eq_repl/
43 lemma unwind_rmap_pap_le (f) (p) (n):
44 n < ▼❘p❘ → (▼[p]𝐢)@⧣❨n❩ = (▼[p]f)@⧣❨n❩.
46 >(tr_pap_eq_repl … (▼[p]f) … (unwind_rmap_decompose …))
47 <tr_compose_pap <tr_pap_pushs_le //