update in functional

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / functional / mf_vpush.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/functional/mf_vpush.ma b/matita/matita/contribs/lambdadelta/apps_2/functional/mf_vpush.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 "apps_2/notation/functional/dotteduparrow_3.ma".
+include "apps_2/functional/flifts_basic.ma".
+include "apps_2/functional/mf_v.ma".
+
+(* MULTIPLE FILLING PUSH ****************************************************)
+
+definition mf_vpush (j) (T) (lv): mf_evaluation ≝
+                    λi. tri … i j (lv i) T (↑[j,1](lv (↓i))).
+
+interpretation "push (multiple filling)"
+  'DottedUpArrow i d lv = (mf_vpush i d lv).
+
+(* Basic properties *********************************************************)
+
+lemma mf_vpush_lt (lv) (j) (T): ∀i. i < j → (⇡[j←T]lv) i = lv i.
+/2 width=1 by tri_lt/ qed-.
+
+lemma mf_vpush_eq: ∀lv,T,i. (⇡[i←T]lv) i = T.
+/2 width=1 by tri_eq/ qed.
+
+lemma mf_vpush_gt: ∀lv,T,j,i. j < i → (⇡[j←T]lv) i = ↑[j,1](lv (↓i)).
+/2 width=1 by tri_gt/ qed-.