update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind_k / unwind2_rmap_closed.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_closed.ma
new file mode 100644 (file)
index 0000000..3d357e0
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_closed.ma
@@ -0,0 +1,101 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/unwind_k/unwind2_rmap_lift.ma".
+include "delayed_updating/unwind_k/unwind2_rmap_eq.ma".
+include "delayed_updating/substitution/lift_rmap_structure.ma".
+include "delayed_updating/syntax/path_closed.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/relocation/nap.ma".
+include "ground/relocation/tr_pushs_tls.ma".
+include "ground/lib/stream_tls_plus.ma".
+include "ground/lib/stream_eq_eq.ma".
+
+(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
+
+(* Destructions with cpp ****************************************************)
+
+lemma nap_plus_unwind2_rmap_closed (o) (e) (f) (q) (m) (n):
+      q ϵ 𝐂❨o,n,e❩ →
+      f＠§❨m+e❩+♭q = ▶[f]q＠§❨m+n❩.
+#o #e #f #q #m #n #Hq elim Hq -q -n //
+#q #n [ #k #_ ] #_ #IH
+[ <depth_d_dx <unwind2_rmap_d_dx
+  <tr_compose_nap <tr_uni_nap //
+| <depth_L_dx <unwind2_rmap_L_dx
+  <tr_nap_push <nplus_succ_dx //
+]
+qed-.
+
+lemma nap_unwind2_rmap_closed (o) (f) (q) (n):
+      q ϵ 𝐂❨o,n,𝟎❩ →
+      f＠§❨𝟎❩+♭q = ▶[f]q＠§❨n❩.
+#o #f #q #n #Hn
+/2 width=2 by nap_plus_unwind2_rmap_closed/
+qed-.
+
+lemma nap_plus_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (m) (n):
+      q ϵ 𝐂❨o,n,𝟎❩ →
+      (⫯▶[f]p)＠§❨m❩+♭q = ▶[f](p●𝗟◗q)＠§❨m+n❩.
+#o #f #p #q #m #n #Hn
+/2 width=2 by nap_plus_unwind2_rmap_closed/
+qed-.
+
+lemma nap_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n,𝟎❩ →
+      ♭q = ▶[f](p●𝗟◗q)＠§❨n❩.
+#o #f #p #q #n #Hn
+>(nplus_zero_sn n)
+<(nap_plus_unwind2_rmap_append_closed_Lq_dx … Hn) -Hn
+<nplus_zero_sn //
+qed-.
+
+lemma tls_succ_plus_unwind2_rmap_push_closed (o) (f) (q) (n):
+      q ϵ 𝐂❨o,n,𝟎❩ →
+      ∀m. ⇂*[m]f ≗ ⇂*[↑(m+n)]▶[⫯f]q.
+#o #f #q #n #Hn elim Hn -q -n //
+#q #n #k #_ #_ #IH #m
+@(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
+>nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold //
+qed-.
+
+lemma tls_succ_unwind2_rmap_push_closed (o) (f) (q) (n):
+      q ϵ 𝐂❨o,n,𝟎❩ →
+      f ≗ ⇂*[↑n]▶[⫯f]q.
+#o #f #q #n #Hn
+/2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
+qed-.
+
+lemma tls_succ_plus_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n,𝟎❩ →
+      ∀m. ⇂*[m]▶[f]p ≗ ⇂*[↑(m+n)]▶[f](p●𝗟◗q).
+#o #f #p #q #n #Hn #m
+/2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
+qed-.
+
+lemma tls_succ_unwind2_rmap_closed (f) (q) (n):
+      q ϵ 𝐂❨Ⓕ,n,𝟎❩ →
+      ⇂f ≗ ⇂*[↑n]▶[f]q.
+#f #q #n #Hn
+@(stream_eq_canc_dx … (stream_tls_eq_repl …))
+[| @(unwind2_rmap_eq_repl … (tr_compose_id_dx …)) | skip ]
+@(stream_eq_trans … (stream_tls_eq_repl …))
+[| @(lift_unwind2_rmap_after … ) | skip ]
+<tr_compose_tls <tr_id_unfold
+@(stream_eq_trans … (tr_compose_eq_repl …))
+[| @(tls_succ_unwind2_rmap_push_closed … Hn) | skip | // | skip ]
+@(stream_eq_trans ????? (tr_compose_id_dx …))
+<tr_pap_succ_nap <(nap_unwind2_rmap_closed … Hn) <nplus_zero_sn
+<lift_rmap_structure <stream_tls_succ <tr_tls_pushs //
+qed-.