matita/matita/contribs/lambdadelta/apps_2/etc/models/vdrop.etc

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "ground_2/lib/functions.ma".
  16 include "apps_2/notation/models/downspoon_3.ma".
  17 include "apps_2/models/model.ma".
  18
  19 (* EVALUATION DROP **********************************************************)
  20
  21 definition vdrop (M): nat → evaluation M → evaluation M ≝
  22                       λj,lv,i. tri … i j (lv i) (lv (↑i)) (lv (↑i)).
  23
  24 interpretation "drop (model evaluation)"
  25    'DownSpoon M i lv = (vdrop M i lv).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma vdrop_lt (M): ∀lv,j,i. i < j → (⫰{M}[j] lv) i = lv i.
  30 /2 width=1 by tri_lt/ qed-.
  31
  32 lemma vdrop_ge (M): ∀lv,j,i. j ≤ i → (⫰{M}[j] lv) i = lv (↑i).
  33 #M #lv #j #i #Hji elim (le_to_or_lt_eq … Hji) -Hji #Hji destruct
  34 [ /2 width=1 by tri_gt/
  35 | /2 width=1 by tri_eq/
  36 ]
  37 qed-.