update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind_k / unwind2_rmap.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/preunwind2_rmap.ma".
+include "delayed_updating/syntax/path.ma".
+
+(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
+
+rec definition unwind2_rmap (f) (p) on p: tr_map ≝
+match p with
+[ list_empty     ⇒ f
+| list_lcons l q ⇒ ▶[unwind2_rmap f q]l
+].
+
+interpretation
+  "tailed unwind (relocation map)"
+  'BlackRightTriangle f p = (unwind2_rmap f p).
+
+(* Basic constructions ******************************************************)
+
+lemma unwind2_rmap_empty (f):
+      f = ▶[f]𝐞.
+// qed.
+
+lemma unwind2_rmap_rcons (f) (p) (l):
+      ▶[▶[f]p]l = ▶[f](p◖l).
+// qed.
+
+lemma unwind2_rmap_d_dx (f) (p) (k:pnat):
+      ▶[f]p∘𝐮❨k❩ = ▶[f](p◖𝗱k).
+// qed.
+
+lemma unwind2_rmap_m_dx (f) (p):
+      ▶[f]p = ▶[f](p◖𝗺).
+// qed.
+
+lemma unwind2_rmap_L_dx (f) (p):
+      (⫯▶[f]p) = ▶[f](p◖𝗟).
+// qed.
+
+lemma unwind2_rmap_A_dx (f) (p):
+      ▶[f]p = ▶[f](p◖𝗔).
+// qed.
+
+lemma unwind2_rmap_S_dx (f) (p):
+      ▶[f]p = ▶[f](p◖𝗦).
+// qed.
+
+(* Constructions with path_append *******************************************)
+
+lemma unwind2_rmap_append (f) (p) (q):
+      ▶[▶[f]p]q = ▶[f](p●q).
+#f #p #q elim q -q // #l #q #IH
+<unwind2_rmap_rcons <unwind2_rmap_rcons //
+qed.
+
+(* Constructions with path_lcons ********************************************)
+
+lemma unwind2_rmap_lcons (f) (p) (l):
+      ▶[▶[f]l]p = ▶[f](l◗p).
+// qed.
+
+lemma unwind2_rmap_d_sn (f) (p) (k:pnat):
+      ▶[f∘𝐮❨k❩]p = ▶[f](𝗱k◗p).
+// qed.
+
+lemma unwind2_rmap_m_sn (f) (p):
+      ▶[f]p = ▶[f](𝗺◗p).
+// qed.
+
+lemma unwind2_rmap_L_sn (f) (p):
+      ▶[⫯f]p = ▶[f](𝗟◗p).
+// qed.
+
+lemma unwind2_rmap_A_sn (f) (p):
+      ▶[f]p = ▶[f](𝗔◗p).
+// qed.
+
+lemma unwind2_rmap_S_sn (f) (p):
+      ▶[f]p = ▶[f](𝗦◗p).
+// qed.