update in ground_2 and models

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / vdrop.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/vdrop.ma b/matita/matita/contribs/lambdadelta/apps_2/models/vdrop.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground_2/lib/functions.ma".
+include "ground_2/lib/exteq.ma".
+include "ground_2/notation/functions/downspoon_2.ma".
+include "apps_2/notation/models/downspoon_3.ma".
+include "apps_2/models/model.ma".
+
+(* EVALUATION DROP **********************************************************)
+
+definition vdrop (M): nat → evaluation M → evaluation M ≝
+                      λj,lv,i. tri … i j (lv i) (lv (↑i)) (lv (↑i)).
+
+interpretation "generic drop (model evaluation)"
+   'DownSpoon M i lv = (vdrop M i lv).
+
+interpretation "drop (model evaluation)"
+   'DownSpoon M lv = (vdrop M O lv).
+
+(* Basic properties *********************************************************)
+
+lemma vdrop_lt (M): ∀lv,j,i. i < j → (⫰{M}[j] lv) i = lv i.
+/2 width=1 by tri_lt/ qed-.
+
+lemma vdrop_ge (M): ∀lv,j,i. j ≤ i → (⫰{M}[j] lv) i = lv (↑i).
+#M #lv #j #i #Hji elim (le_to_or_lt_eq … Hji) -Hji #Hji destruct
+[ /2 width=1 by tri_gt/
+| /2 width=1 by tri_eq/
+]
+qed-.
+
+lemma vdrop_ext (M): ∀i. compatible_2 … (vdrop M i) (exteq …) (exteq …).
+#M #i #lv1 #lv2 #Hlv12 #j elim (lt_or_ge j i) #Hji
+[ >vdrop_lt // >vdrop_lt //
+| >vdrop_ge // >vdrop_ge //
+]
+qed.