proposition: Lemma subspace_pm_ball_sym x y (e : R) : subspace_ball x e y -> subspace_ball y e x.
proof: Proof. rewrite /subspace_ball; case: ifP => //= /asboolP ?. by move=> [] Ay /ball_sym yBx; case: ifP => /asboolP. by move=> ->; case: ifP => /asboolP. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed