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

Lemma same_support_change_lock {A} (lset : AMap.t A) l x : AMap.find l lset <> None -> lset_same_support lset (AMap.add l x lset).