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

Lemma linear_inter_spec s1 s2 x `(Ok s1, Ok s2) :
InT x (linear_inter s1 s2) <-> InT x s1 /\ InT x s2.