∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : SeminormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (f : E → F),
  IsLinearMap 𝕜 f ∧ Continuous f ↔ IsBoundedLinearMap 𝕜 f