Definition only_blocks {S: block -> Prop} (S_dec: forall b, {S b}+{~S b}) (w: rmap) : rmap.
refine (proj1_sig (make_rmap (fun loc => if S_dec (fst loc) then w @ loc else core (w @ loc))
_ (level w) _ (ghost_of_approx w))).

Lemma level_only_blocks: forall {S} S_dec phi,
level (@only_blocks S S_dec phi) = level phi.