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 *)
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15 include "delayed_updating/unwind/unwind2_rmap_closed.ma".
16 include "delayed_updating/unwind/unwind2_rmap_guard.ma".
18 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
20 (* Crucial constructions with tr_uni ****************************************)
22 (* Note: crux of the commutation between unwind and balanced focused reduction *)
23 lemma unwind2_rmap_uni_crux (f) (p) (b) (q) (m) (n):
24 p ϵ 𝐆 → b ϵ 𝐂❨Ⓕ,m❩ → q ϵ 𝐂❨Ⓕ,n❩ →
25 (𝐮❨↑(♭b+♭q)❩ ∘ ▶[⫯f]p ≗ ▶[⫯f](p●𝗔◗b●𝗟◗q) ∘ 𝐮❨↑(m+n)❩).
26 #f #p #b #q #m #n #Hp #Hm #Hn
27 <list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
28 >list_append_rcons_sn >(list_append_rcons_sn … b)
29 @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
30 @(stream_eq_trans ????? (tr_compose_eq_repl …))
31 [| @tls_succ_plus_unwind2_rmap_append_closed_Lq_dx // | skip
32 | <nap_plus_unwind2_rmap_append_closed_Lq_dx // | skip
34 @tr_eq_inv_nap_zero_tl_bi
35 [ <tr_compose_nap <tr_compose_nap <tr_uni_nap <tr_uni_nap
36 <nap_zero_unwind2_rmap_push_guard // <nplus_zero_sn
37 >nsucc_unfold >nplus_succ_dx >nplus_succ_dx <nplus_assoc
38 >tr_nap_plus_dx <unwind2_rmap_append
39 <nap_plus_unwind2_rmap_closed [|*: /2 width=2 by pcc_A_sn/ ]
40 <nap_zero_unwind2_rmap_push_guard //
41 | @(stream_eq_canc_sn … (tr_tl_compose_uni_sn …))
42 @(stream_eq_trans ????? (tr_tl_compose_uni_sn …))
43 >stream_tls_succ <unwind2_rmap_append <unwind2_rmap_push_guard
44 /2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/