Independent branchings in acyclic diagraphs

Let D be a finite directed acyclic multigraph and t be a vertex of D such that for each other vertex x of D, there are n pairwise openly disjoint paths in D from x to t. It is proved that there exist n spanning trees B1,…,Bn in D directed toward t such that for each vertex x ≠ t of D, the n paths from x to t in B1,…,Bn are pairwise openly disjoint.