Definition AbsRing_ball (x : K) (eps : R) (y : K) := abs (minus y x) < eps.

(* Specifications: *)
Lemma AbsRing_ball_center : forall (x : K) (e : posreal), AbsRing_ball x e x.
Lemma AbsRing_ball_sym : forall (x y : K) (e : R), AbsRing_ball x e y -> AbsRing_ball y e x.
Lemma AbsRing_ball_triangle : forall (x y z : K) (e1 e2 : R), AbsRing_ball x e1 y -> AbsRing_ball y e2 z -> AbsRing_ball x (e1 + e2) z.