Section Lifting.
Variable (sig : Type).
Variable (m n : nat).
(* [P] is the premise of the lifted machine [M@I]. *)
Variable (P : @SpecV sig n).
Variable (I : Vector.t (Fin.t n) m). (* [m<=n] *)
Hypothesis (HI : dupfree I).
(* We want to extract from [P] the premise [P'] for [M] *)
Definition Downlift : @SpecV sig m :=
(select I P).

Lemma tape_fulfill_Downlift_select P' tp :
tspec (P',P) tp ->
tspec (P',Downlift) (select I tp).