(** Direct reflexive-transitive closure is equivalent to transitivity by right-step extension *)

(* Specifications: *)
Lemma clos_rtn1_rt : forall x y,
clos_refl_trans_n1 R x y -> clos_refl_trans R x y.
Lemma clos_rt_rtn1 :  forall x y,
clos_refl_trans R x y -> clos_refl_trans_n1 R x y.
Lemma clos_rt_rtn1_iff : forall x y,
clos_refl_trans R x y <-> clos_refl_trans_n1 R x y.