∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_4} {F : Type u_5} {𝓕 : Type u_8} [inst : SeminormedAddCommGroup E]
  [inst_1 : SeminormedAddCommGroup F] [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NontriviallyNormedField 𝕜₂]
  [inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : FunLike 𝓕 E F]
  [SemilinearMapClass 𝓕 σ₁₂ E F] [RingHomSurjective σ₁₂] {f : 𝓕} (x : F) {r : ℝ},
  0 < r → (Metric.closedBall x r ⊆ Set.range ⇑f ↔ Function.Surjective ⇑f)