#[global]
Instance inter_ok s1 s2 `(Ok s1, Ok s2) : Ok (inter s1 s2).

Lemma diff_spec_ok : forall s1 s2 `{Ok s1, Ok s2}, Ok (diff s1 s2) /\ (forall y, InT y (diff s1 s2) <-> InT y s1 /\ ~InT y s2).