(*s [(CG_leq x y)] is true when there is a path from [x] to [y] *)

Definition CG_leq (x y : ad) :=
  match ad_simple_path_dist x y with
  | Some _ => true
  | _ => false
  end.

(* Specifications: *)
Lemma CG_leq_refl : forall x : ad, CG_leq x x = true.
Lemma CG_leq_trans : forall x y z : ad, CG_leq x y = true -> CG_leq y z = true -> CG_leq x z = true.