update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind_k / unwind2_rmap_depth.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_depth.ma
new file mode 100644 (file)
index 0000000..6aa48f2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_depth.ma
@@ -0,0 +1,58 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_path_append.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/relocation/tr_id_compose.ma".
+include "ground/relocation/tr_compose_compose.ma".
+include "ground/relocation/tr_compose_eq.ma".
+include "ground/relocation/xap.ma".
+include "ground/lib/stream_eq_eq.ma".
+
+(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
+
+(* Constructions with depth *************************************************)
+
+lemma unwind2_rmap_decompose (p) (f):
+      ▶[f]p ≗ (⫯*[♭p]f)∘(▶[𝐢]p).
+#p elim p -p
+[ #f <unwind2_rmap_empty <unwind2_rmap_empty <tr_pushs_zero //
+| * [ #k ] #p #IH #f //
+  [ <unwind2_rmap_d_dx <unwind2_rmap_d_dx <depth_d_dx
+    @(stream_eq_trans … (tr_compose_assoc …))
+    /2 width=1 by tr_compose_eq_repl/
+  | <unwind2_rmap_L_dx <unwind2_rmap_L_dx <depth_L_dx
+    <tr_pushs_succ <tr_compose_push_bi
+    /2 width=1 by tr_push_eq_repl/
+  ]
+]
+qed.
+
+lemma unwind2_rmap_pap_le (f) (p) (h):
+      ▶[𝐢]p＠⧣❨h❩ < ↑♭p → ▶[𝐢]p＠⧣❨h❩ = ▶[f]p＠⧣❨h❩.
+#f #p #h #Hh
+>(tr_pap_eq_repl … (▶[f]p) … (unwind2_rmap_decompose …))
+<tr_compose_pap <tr_pap_pushs_le //
+qed.
+
+lemma unwind2_rmap_xap_le (f) (p) (n):
+      ▶[𝐢]p＠❨n❩ ≤ ♭p → ▶[𝐢]p＠❨n❩ = ▶[f]p＠❨n❩.
+(*
+#f #p * // #h <tr_xap_ninj #Hh
+>unwind2_rmap_pap_le
+*)
+#f #p #n #Hn
+>(tr_xap_eq_repl … (▶[f]p) … (unwind2_rmap_decompose …))
+<tr_compose_xap <tr_xap_pushs_le //
+qed-.