The set of distances in seminormal weakly Krull monoids

The set of distances of a monoid or of a domain is the set of all $d \in \mathbb N$withthefollowingproperty:thereareirreducibleelements$u_1, \ldots, u_k, v_1, \ldots, v_{k+d}$suchthat$u_1 \cdot \ldots \cdot u_k = v_1 \cdot \ldots \cdot v_{k+d}$,but$u_1 \cdot \ldots \cdot u_k$ cannot be written as a product of $l$ irreducible elements for any $l$ with $k<l<k+d$. We show that the set of distances is an interval for certain seminormal weakly Krull monoids which include seminormal orders in holomorphy rings of global fields.