update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / relocation / tr_minus.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus.ma b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus.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 "ground/arith/pnat_minus.ma".
+include "ground/arith/nat_minus.ma".
+include "ground/relocation/tr_map.ma".
+
+(* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
+
+corec definition tr_minus: nat → tr_map → tr_map.
+* [ #f @f ] #q * #p #f
+@((p-q)⨮(tr_minus (ninj (↑q)-ninj p) f))
+defined.
+
+interpretation
+  "right minus (total relocation maps)"
+  'minus f n = (tr_minus n f).
+
+(* Basic constructions ******************************************************)
+
+lemma tr_minus_zero_dx (f):
+      f = f - 𝟎 .
+* #f #p <(stream_unfold … ((f⨮p)-𝟎)) //
+qed.
+
+lemma tr_minus_cons_inj (f) (p) (q):
+      (p-q)⨮(f-(ninj (↑q)-ninj p)) = (p⨮f)-(ninj q).
+#f #p #q <(stream_unfold … ((p⨮f)-(ninj q))) //
+qed.