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.