#[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 diff_list_spec x l1 l2 acc :
sort X.lt (rev l1) ->
sort X.lt (rev l2) ->
(InA X.eq x (diff_list l1 l2 acc) <->
(InA X.eq x l1 /\ ~InA X.eq x l2) \/ InA X.eq x acc).