milestone update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / fr2_plus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_plus.ma b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_plus.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/nat_minus_plus.ma".
+include "ground/relocation/fr2_map.ma".
+
+(* ADDITION FOR FINITE RELOCATION MAPS WITH PAIRS ******************************)
+
+(* Note: this is pushs *)
+(*** pluss *)
+rec definition fr2_plus (f:fr2_map) (n:nat) on f ≝ match f with
+[ fr2_nil        ⇒ ◊
+| fr2_cons d h f ⇒ ❨d+n,h❩;fr2_plus f n
+].
+
+interpretation
+  "plus (finite relocation maps with pairs)"
+  'plus f n = (fr2_plus f n).
+
+(* Basic properties *********************************************************)
+
+(*** pluss_SO2 *)
+lemma fr2_plus_cons_unit (d) (h) (f):
+      ((❨d,h❩;f)+𝟏) = ❨↑d,h❩;f+𝟏.
+normalize // qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+(*** pluss_inv_nil2 *)
+lemma fr2_plus_inv_nil_dx (n) (f):
+      f+n = ◊ → f = ◊.
+#n * // normalize
+#d #h #f #H destruct
+qed.
+
+(*** pluss_inv_cons2 *)
+lemma fr2_plus_inv_cons_dx (n) (d) (h) (f2) (f):
+      f + n = ❨d,h❩;f2 →
+      ∃∃f1. f1+n = f2 & f = ❨d-n,h❩;f1.
+#n #d #h #f2 *
+[ normalize #H destruct
+| #d1 #h1 #f1 whd in ⊢ (??%?→?); #H destruct
+  <nminus_plus_sn_refl_sn /2 width=3 by ex2_intro/
+]
+qed-.