ground_2 milestone: multiple relocation with lists of booleans

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / mr2_plus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_plus.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_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_2/relocation/mr2.ma".
+
+(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
+
+let rec pluss (cs:mr2) (i:nat) on cs ≝ match cs with
+[ nil2         ⇒ ◊
+| cons2 l m cs ⇒ {l + i, m} @ pluss cs i
+].
+
+interpretation "plus (multiple relocation with pairs)"
+   'plus x y = (pluss x y).
+
+(* Basic properties *********************************************************)
+
+lemma pluss_SO2: ∀l,m,cs. ({l, m} @ cs) + 1 = {⫯l, m} @ cs + 1.
+normalize // qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma pluss_inv_nil2: ∀i,cs. cs + i = ◊ → cs = ◊.
+#i * // normalize
+#l #m #cs #H destruct
+qed.
+
+lemma pluss_inv_cons2: ∀i,l,m,cs2,cs. cs + i = {l, m} @ cs2 →
+                       ∃∃cs1. cs1 + i = cs2 & cs = {l - i, m} @ cs1.
+#i #l #m #cs2 *
+[ normalize #H destruct
+| #l1 #m1 #cs1 whd in ⊢ (??%?→?); #H destruct
+  <minus_plus_m_m /2 width=3 by ex2_intro/
+]
+qed-.