Notation trans_clos := (clos_trans A R).

(* Specifications: *)
Lemma incl_clos_trans : inclusion A R trans_clos.
Lemma Acc_clos_trans : forall x:A, Acc R x -> Acc trans_clos x.
Lemma Acc_inv_trans : forall x y:A, trans_clos y x -> Acc R x -> Acc R y.
Theorem wf_clos_trans : well_founded R -> well_founded trans_clos.