Section RtRft.
Variable A:Type.
Variable R:relation A.
Let Rt := clos_trans A R.
Let Rft := clos_refl_trans A R.

(* Specifications: *)
Lemma Rt_Rft : forall x y, Rt x y -> Rft x y.
Lemma Rt_Rft_trans : forall x y z, Rt x y -> Rft y z -> Rt x z.
Lemma Rft_Rt_trans : forall x y z, Rft x y -> Rt y z -> Rt x z.
Lemma transpose_clos_trans : forall A R x y,
clos_trans A (transp A R) x y <-> transp A (clos_trans A R) x y.