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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "apps_2/notation/functional/dotteduparrow_3.ma".
16 include "apps_2/functional/flifts_basic.ma".
17 include "apps_2/functional/mf_v.ma".
19 (* MULTIPLE FILLING PUSH ****************************************************)
21 definition mf_vpush (j) (T) (lv): mf_evaluation ≝
22 λi. tri … i j (lv i) T (↑[j,1](lv (↓i))).
24 interpretation "push (multiple filling)"
25 'DottedUpArrow i d lv = (mf_vpush i d lv).
27 (* Basic properties *********************************************************)
29 lemma mf_vpush_lt (lv) (j) (T): ∀i. i < j → (⇡[j←T]lv) i = lv i.
30 /2 width=1 by tri_lt/ qed-.
32 lemma mf_vpush_eq: ∀lv,T,i. (⇡[i←T]lv) i = T.
33 /2 width=1 by tri_eq/ qed.
35 lemma mf_vpush_gt: ∀lv,T,j,i. j < i → (⇡[j←T]lv) i = ↑[j,1](lv (↓i)).
36 /2 width=1 by tri_gt/ qed-.