(** q represents a basis big enough so that all the sequence x=x0 R x1 R ... R xn = y can be
      encoded as the digits of c in base q *)

  Definition rel_iter_seq n x y := exists q c, is_seq R c q n /\ is_digit c q 0 x /\ is_digit c q n y.

(* Specifications: *)
Lemma rel_iter_seq_iter n x y : rel_iter_seq n x y -> rel_iter R n x y.
Lemma rel_iter_iter_seq n x y : rel_iter R n x y -> rel_iter_seq n x y.
Theorem rel_iter_seq_equiv n x y : rel_iter R n x y <-> rel_iter_seq n x y.