∀ {𝕜 : Type u_1} {𝕜' : Type u_2} {E : Type u_3} {F : Type u_4} [inst : AddCommGroup E] [inst_1 : TopologicalSpace E]
  [inst_2 : IsTopologicalAddGroup E] [inst_3 : AddCommGroup F] [inst_4 : TopologicalSpace F]
  [inst_5 : NontriviallyNormedField 𝕜] [inst_6 : Module 𝕜 E] [inst_7 : ContinuousSMul 𝕜 E] [inst_8 : NormedField 𝕜']
  [inst_9 : Module 𝕜' F] {σ : 𝕜 →+* 𝕜'} [inst_10 : RingHomIsometric σ] [inst_11 : IsTopologicalAddGroup F]
  {f : E →ₛₗ[σ] F} {h : ∃ V ∈ nhds 0, Bornology.IsVonNBounded 𝕜' (⇑f '' V)}, ↑(f.clmOfExistsBoundedImage h) = f