#[global]
Instance diff_inter_ok s1 s2 `(Ok s1, Ok s2) :
Ok (linear_diff s1 s2).
#[global]
Instance fold_remove_ok s1 s2 `(Ok s2) :
Ok (fold remove s1 s2).
#[global]
Instance diff_ok s1 s2 `(Ok s1, Ok s2) : Ok (diff s1 s2).

Lemma linear_diff_spec s1 s2 x `(Ok s1, Ok s2) :
InT x (linear_diff s1 s2) <-> InT x s1 /\ ~InT x s2.