proposition: Lemma prod_ball_triangle x y z (e1 e2 : R) : prod_ball x e1 y -> prod_ball y e2 z -> prod_ball x (e1 + e2) z.
proof: Proof. by move=> [bxy1 bxy2] [byz1 byz2]; split; apply: ball_triangle; eassumption. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed