(*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.