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).