1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 include "ground_2/lib/functions.ma".
16 include "ground_2/lib/exteq.ma".
17 include "ground_2/notation/functions/downspoon_2.ma".
18 include "apps_2/notation/models/downspoon_3.ma".
19 include "apps_2/models/model.ma".
21 (* EVALUATION DROP **********************************************************)
23 definition vdrop (M): nat → evaluation M → evaluation M ≝
24 λj,lv,i. tri … i j (lv i) (lv (↑i)) (lv (↑i)).
26 interpretation "generic drop (model evaluation)"
27 'DownSpoon M i lv = (vdrop M i lv).
29 interpretation "drop (model evaluation)"
30 'DownSpoon M lv = (vdrop M O lv).
32 (* Basic properties *********************************************************)
34 lemma vdrop_lt (M): ∀lv,j,i. i < j → (⫰{M}[j] lv) i = lv i.
35 /2 width=1 by tri_lt/ qed-.
37 lemma vdrop_ge (M): ∀lv,j,i. j ≤ i → (⫰{M}[j] lv) i = lv (↑i).
38 #M #lv #j #i #Hji elim (le_to_or_lt_eq … Hji) -Hji #Hji destruct
39 [ /2 width=1 by tri_gt/
40 | /2 width=1 by tri_eq/
44 lemma vdrop_ext (M): ∀i. compatible_2 … (vdrop M i) (exteq …) (exteq …).
45 #M #i #lv1 #lv2 #Hlv12 #j elim (lt_or_ge j i) #Hji
46 [ >vdrop_lt // >vdrop_lt //
47 | >vdrop_ge // >vdrop_ge //