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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "ground_2/lib/functions.ma".
16 include "apps_2/notation/models/downspoon_3.ma".
17 include "apps_2/models/model.ma".
19 (* EVALUATION DROP **********************************************************)
21 definition vdrop (M): nat → evaluation M → evaluation M ≝
22 λj,lv,i. tri … i j (lv i) (lv (↑i)) (lv (↑i)).
24 interpretation "drop (model evaluation)"
25 'DownSpoon M i lv = (vdrop M i lv).
27 (* Basic properties *********************************************************)
29 lemma vdrop_lt (M): ∀lv,j,i. i < j → (⫰{M}[j] lv) i = lv i.
30 /2 width=1 by tri_lt/ qed-.
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/