update in grond_2 and models

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / rtmap_basic.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_basic.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_basic.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_2/notation/functions/basic_2.ma".
+include "ground_2/relocation/rtmap_at.ma".
+
+(* RELOCATION MAP ***********************************************************)
+
+definition basic: nat → nat → rtmap ≝ λm,n. ⫯*[m] 𝐔❴n❵.
+
+interpretation "basic relocation (rtmap)"
+   'Basic m n = (basic m n).
+
+(* Prioerties with application **********************************************)
+
+lemma at_basic_lt: ∀m,n,i. i < m → @⦃i, 𝐁❴m,n❵⦄ ≘ i.
+#m elim m -m [ #n #i #H elim (lt_zero_false … H) ]
+#m #IH #n * [ /2 width=2 by refl, at_refl/ ]
+#i #H lapply (lt_S_S_to_lt … H) -H /3 width=7 by refl, at_push/
+qed.
+
+lemma at_basic_ge: ∀m,n,i. m ≤ i → @⦃i, 𝐁❴m,n❵⦄ ≘ n+i.
+#m elim m -m //
+#m #IH #n #j #H
+elim (le_inv_S1 … H) -H #i #Hmi #H destruct
+/3 width=7 by refl, at_push/
+qed.
+
+(* Inversion lemmas with application ****************************************)
+
+lemma at_basic_inv_lt: ∀m,n,i,j. i < m → @⦃i, 𝐁❴m,n❵⦄ ≘ j → i = j.
+/3 width=4 by at_basic_lt, at_mono/ qed-.
+
+lemma at_basic_inv_ge: ∀m,n,i,j. m ≤ i → @⦃i, 𝐁❴m,n❵⦄ ≘ j → n+i = j.
+/3 width=4 by at_basic_ge, at_mono/ qed-.