update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_eq.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_eq.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/lib/stream_eq.ma".
+
+(* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
+
+(* Constructions with tr_eq *************************************************)
+
+corec lemma tr_minus_eq_repl (n):
+            stream_eq_repl … (λf1,f2. f1-n ≗ f2-n).
+cases n -n
+[ #f1 #f2 #Hf -tr_minus_eq_repl //
+| #q * #p1 #f1 * #p2 #f2 #Hf
+  cases (stream_eq_inv_cons_bi … Hf) -Hf  [|*: // ] * #Hf -p2
+  cases tr_minus_cons_inj cases tr_minus_cons_inj
+  @stream_eq_cons //
+  @tr_minus_eq_repl //
+]
+qed.