∀ {𝕜₁ : Type u_6} {𝕜₂ : Type u_1} {𝕜₃ : Type u_2} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂]
  [inst_2 : NormedField 𝕜₃] {σ : 𝕜₁ →+* 𝕜₂} {τ : 𝕜₂ →+* 𝕜₃} {ρ : 𝕜₁ →+* 𝕜₃} [inst_3 : RingHomCompTriple σ τ ρ]
  {E : Type u_5} {F : Type u_3} (G : Type u_4) [inst_4 : AddCommGroup E] [inst_5 : Module 𝕜₁ E]
  [inst_6 : AddCommGroup F] [inst_7 : Module 𝕜₂ F] [inst_8 : AddCommGroup G] [inst_9 : Module 𝕜₃ G]
  [inst_10 : TopologicalSpace E] [inst_11 : TopologicalSpace F] [inst_12 : TopologicalSpace G]
  [inst_13 : IsTopologicalAddGroup G] [inst_14 : ContinuousConstSMul 𝕜₃ G] [inst_15 : RingHomSurjective σ]
  [inst_16 : RingHomIsometric σ] (L : E →SL[σ] F) (x y : UniformConvergenceCLM τ G {S | Bornology.IsVonNBounded 𝕜₂ S}),
  (↑(ContinuousLinearMap.precompUniformConvergenceCLM G {S | Bornology.IsVonNBounded 𝕜₁ S}
            {S | Bornology.IsVonNBounded 𝕜₂ S} L ⋯)).toFun
      (x + y) =
    (↑(ContinuousLinearMap.precompUniformConvergenceCLM G {S | Bornology.IsVonNBounded 𝕜₁ S}
              {S | Bornology.IsVonNBounded 𝕜₂ S} L ⋯)).toFun
        x +
      (↑(ContinuousLinearMap.precompUniformConvergenceCLM G {S | Bornology.IsVonNBounded 𝕜₁ S}
              {S | Bornology.IsVonNBounded 𝕜₂ S} L ⋯)).toFun
        y