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

Lemma sparsity_same_support {A} (lset1 lset2 : AMap.t A) : lset_same_support lset1 lset2 -> lock_sparsity lset1 -> lock_sparsity lset2.