initial definition of λδ model

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / model_push.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 "apps_2/notation/models/upspoon_4.ma".
+include "apps_2/notation/models/upspoon_3.ma".
+include "apps_2/models/model.ma".
+
+(* MODEL ********************************************************************)
+
+definition push (M): nat → dd M → evaluation M → evaluation M ≝
+                     λj,d,lv,i. tri … i j (lv i) d (lv (↓i)).
+
+interpretation "generic push (model evaluation)"
+   'UpSpoon M i d lv = (push M i d lv).
+
+interpretation "push (model evaluation)"
+   'UpSpoon M d lv = (push M O d lv).
+
+(* Basic properties *********************************************************)
+
+lemma push_lt: ∀M,lv,d,j,i. i < j → (⫯{M}[j←d] lv) i = lv i.
+/2 width=1 by tri_lt/ qed-.
+
+lemma push_eq: ∀M,lv,d,i. (⫯{M}[i←d] lv) i = d.
+/2 width=1 by tri_eq/ qed-.
+
+lemma push_gt: ∀M,lv,d,j,i. j < i → (⫯{M}[j←d] lv) i = lv (↓i).
+/2 width=1 by tri_gt/ qed-.