matita/matita/contribs/lambdadelta/apps_2/functional/mf_vpush.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "apps_2/notation/functional/dotteduparrow_3.ma".
  16 include "apps_2/functional/flifts_basic.ma".
  17 include "apps_2/functional/mf_v.ma".
  18
  19 (* MULTIPLE FILLING PUSH ****************************************************)
  20
  21 definition mf_vpush (j) (T) (lv): mf_evaluation ≝
  22                     λi. tri … i j (lv i) T (↑[j,1](lv (↓i))).
  23
  24 interpretation "push (multiple filling)"
  25   'DottedUpArrow i d lv = (mf_vpush i d lv).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma mf_vpush_lt (lv) (j) (T): ∀i. i < j → (⇡[j←T]lv) i = lv i.
  30 /2 width=1 by tri_lt/ qed-.
  31
  32 lemma mf_vpush_eq: ∀lv,T,i. (⇡[i←T]lv) i = T.
  33 /2 width=1 by tri_eq/ qed.
  34
  35 lemma mf_vpush_gt: ∀lv,T,j,i. j < i → (⇡[j←T]lv) i = ↑[j,1](lv (↓i)).
  36 /2 width=1 by tri_gt/ qed-.