update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / multiple / mr2_plus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_plus.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_plus.ma
new file mode 100644 (file)
index 0000000..fe66fa1
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_plus.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "basic_2A/multiple/mr2.ma".
+
+(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
+
+let rec pluss (cs:list2 nat nat) (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 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 #H destruct /2 width=3 by ex2_intro/
+]
+qed-.