intros.
generalize z H0.
elim H; intros; auto.
apply t_trans with y0; auto with pts.
Qed.

Lemma step_clos_rt_trans :
forall (A : Set) (R : A -> A -> Prop) (x y z : A),
clos_trans _ R x y -> clos_refl_trans _ R y z -> clos_trans _ R x z.