update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pn.ma b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pn.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pn.ma
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/tr_minus.ma".
+include "ground/relocation/tr_pn.ma".
+include "ground/arith/nat_succ.ma".
+
+(* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
+
+(* Constructions with tr_push ***********************************************)
+
+lemma tr_minus_push_succ (f) (n):
+      (⫯(f-↑n)) = (⫯f)-↑n.
+#f #n <tr_minus_cons_inj //
+qed.
+
+(* Constructions with tr_next ***********************************************)
+
+lemma tr_minus_next_succ (n) (f:tr_map):
+      f-n = (↑f)-↑n.
+* [| #n ] * #p #f
+<tr_minus_cons_inj //
+<tr_minus_cons_inj //
+qed.