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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-.