Definition lset_same_support {A} (lset1 lset2 : AMap.t A) :=
  forall loc,
    AMap.find loc lset1 = None <->
    AMap.find loc lset2 = None.

Lemma lset_same_support_map {A} m (f : A -> A) : lset_same_support (AMap.map (option_map f) m) m.