Section AbsRing_UniformSpace.
Variable K : AbsRing.
Definition AbsRing_ball (x : K) (eps : R) (y : K) := abs (minus y x) < eps.

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.