partial commit in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift_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/substitution/prelift_rmap.ma".
+include "delayed_updating/syntax/path.ma".
+
+(* LIFT FOR RELOCATION MAP **************************************************)
+
+rec definition lift_rmap (f) (p) on p: tr_map ≝
+match p with
+[ list_empty     ⇒ f
+| list_lcons l q ⇒ ↑[l](lift_rmap f q)
+].
+
+interpretation
+  "lift (relocation map)"
+  'UpArrow p f = (lift_rmap f p).
+
+(* Basic constructions ******************************************************)
+
+lemma lift_rmap_empty (f):
+      f = ↑[𝐞]f.
+// qed.
+
+lemma lift_rmap_rcons (f) (p) (l):
+      ↑[l]↑[p]f = ↑[p◖l]f.
+// qed.
+
+lemma lift_rmap_d_dx (f) (p) (k:pnat):
+      ⇂*[k](↑[p]f) = ↑[p◖𝗱k]f.
+// qed.
+
+lemma lift_rmap_m_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗺]f.
+// qed.
+
+lemma lift_rmap_L_dx (f) (p):
+      (⫯↑[p]f) = ↑[p◖𝗟]f.
+// qed.
+
+lemma lift_rmap_A_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗔]f.
+// qed.
+
+lemma lift_rmap_S_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗦]f.
+// qed.
+
+(* Constructions with path_append *******************************************)
+
+lemma lift_rmap_append (p) (q) (f):
+      ↑[q]↑[p]f = ↑[p●q]f.
+#p #q elim q -q //
+qed.
+
+(* Constructions with path_lcons ********************************************)
+
+lemma lift_rmap_lcons (f) (p) (l):
+      ↑[p]↑[l]f = ↑[l◗p]f.
+// qed.
+
+lemma lift_rmap_d_sn (f) (p) (k:pnat):
+      ↑[p](⇂*[k]f) = ↑[𝗱k◗p]f.
+// qed.
+
+lemma lift_rmap_m_sn (f) (p):
+      ↑[p]f = ↑[𝗺◗p]f.
+// qed.
+
+lemma lift_rmap_L_sn (f) (p):
+      ↑[p](⫯f) = ↑[𝗟◗p]f.
+// qed.
+
+lemma lift_rmap_A_sn (f) (p):
+      ↑[p]f = ↑[𝗔◗p]f.
+// qed.
+
+lemma lift_rmap_S_sn (f) (p):
+      ↑[p]f = ↑[𝗦◗p]f.
+// qed.