Variable TaX: relation2 X X'.
Variable TaY: relation2 Y Y'.
Variable S' : relation2 X' X'.
Variable R' : relation2 X' Y'.
Let SR' := comp (star S') R'.
Let TAX := comp (star TX) TaX.
Let TAY := comp (star TY) TaY.
Hypothesis HT:  diagram TaX S TAX (star S').
Hypothesis HRT: diagram TaX R TAY SR'.

(** Corollary 4.6 *)
Lemma diagram_star_wf: commute TX S.
End StarWf.