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))).

(* Specifications: *)
Lemma join_only_blocks:
forall {S} S_dec phi, identity (ghost_of phi) -> join (@only_blocks S S_dec phi)
(only_blocks (not_dec S_dec) phi) phi.
Lemma Exists_dec: forall {T} (f: T -> Prop)(f_dec: forall x, {f x}+{~f x}) (l: list T),
{Exists f l}+{~Exists f l}.
Lemma only_blocks_at: forall {S} S_dec phi loc,
@only_blocks S S_dec phi @ loc =
if S_dec (fst loc) then phi @ loc else core (phi @ loc).
Lemma level_only_blocks: forall {S} S_dec phi,
level (@only_blocks S S_dec phi) = level phi.