Definition AbsRing_UniformSpace_mixin :=
  UniformSpace.Mixin _ _ AbsRing_ball_center AbsRing_ball_sym AbsRing_ball_triangle.Canonical AbsRing_UniformSpace :=
  UniformSpace.Pack K AbsRing_UniformSpace_mixin K.Definition fct_ball (x : T -> U) (eps : R) (y : T -> U) :=
  forall t : T, ball (x t) eps (y t).

Lemma fct_ball_triangle : forall (x y z : T -> U) (e1 e2 : R), fct_ball x e1 y -> fct_ball y e2 z -> fct_ball x (e1 + e2) z.