matita/matita/contribs/lambdadelta/apps_2/models/model_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 "ground/lib/functions.ma".
  16 include "apps_2/notation/models/upspoon_4.ma".
  17 include "apps_2/models/model.ma".
  18
  19 (* MODEL ********************************************************************)
  20
  21 definition vpush (M): nat → dd M → evaluation M → evaluation M ≝
  22                       λj,d,lv,i. tri … i j (lv i) d (lv (↓i)).
  23
  24 interpretation "push (model evaluation)"
  25    'UpSpoon M i d lv = (vpush M i d lv).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma vpush_lt (M): ∀lv,d,j,i. i < j → (⫯{M}[j←d] lv) i = lv i.
  30 /2 width=1 by tri_lt/ qed-.
  31
  32 lemma vpush_eq (M): ∀lv,d,i. (⫯{M}[i←d] lv) i = d.
  33 /2 width=1 by tri_eq/ qed-.
  34
  35 lemma vpush_gt (M): ∀lv,d,j,i. j < i → (⫯{M}[j←d] lv) i = lv (↓i).
  36 /2 width=1 by tri_gt/ qed-.