Definition Upw_to_TRRGraph (T : Tree) (x : pr11 T) : TRRGraph := pr1 (Upw_to_PointedGraph T x) ,, pr12 (Upw_to_PointedGraph T x) ,, pr22 (Upw_to_PointedGraph T x) ,, Upw_reflexive T x ,, Upw_transitive T x ,, Upw_rooted T x.