(**************************************************************************)
include "ground_2/lib/functions.ma".
-include "ground_2/lib/exteq.ma".
include "apps_2/notation/models/upspoon_4.ma".
-include "apps_2/notation/models/upspoon_3.ma".
include "apps_2/models/model.ma".
-
(* MODEL ********************************************************************)
definition vlift (M): nat → dd M → evaluation M → evaluation M ≝
λj,d,lv,i. tri … i j (lv i) d (lv (↓i)).
-interpretation "generic lift (model evaluation)"
- 'UpSpoon M i d lv = (vlift M i d lv).
-
interpretation "lift (model evaluation)"
- 'UpSpoon M d lv = (vlift M O d lv).
+ 'UpSpoon M i d lv = (vlift M i d lv).
(* Basic properties *********************************************************)
lemma vlift_gt (M): ∀lv,d,j,i. j < i → (⫯{M}[j←d] lv) i = lv (↓i).
/2 width=1 by tri_gt/ qed-.
-
-lemma vlift_ext (M): ∀i. compatible_3 … (vlift M i) (eq …) (exteq …) (exteq …).
-#m #i #d1 #d2 #Hd12 #lv1 #lv2 #HLv12 #j
-elim (lt_or_eq_or_gt j i) #Hij destruct
-[ >vlift_lt // >vlift_lt //
-| >vlift_eq >vlift_eq //
-| >vlift_gt // >vlift_gt //
-]
-qed.