#[global]
Instance linear_union_ok s1 s2 `(Ok s1, Ok s2) :
Ok (linear_union s1 s2).
#[global]
Instance fold_add_ok s1 s2 `(Ok s1, Ok s2) :
Ok (fold add s1 s2).
#[global]
Instance union_ok s1 s2 `(Ok s1, Ok s2) : Ok (union s1 s2).

Lemma linear_union_spec s1 s2 x :
InT x (linear_union s1 s2) <-> InT x s1 \/ InT x s2.