Definition RTStep_left : forall x y z : T, R x y -> rightTrans y z -> rightTrans x z.

(* Specifications: *)
Theorem makeTrans_idem : forall s s', makeTrans (makeTrans R) s s' <-> makeTrans R s s'.
Theorem makeTrans_makeRefl_comm : forall s s', makeTrans (makeRefl R) s s' <-> makeRefl (makeTrans R) s s'.
Theorem makeRefl_idem : forall s s', makeRefl (makeRefl R) s s' <-> makeRefl R s s'.