∀ {k : Type u_10} {P₁ : Type u_11} {P₂ : Type u_12} {P₃ : Type u_13} {V₁ : Type u_15} {V₂ : Type u_16} {V₃ : Type u_17}
  [inst : Ring k] [inst_1 : AddCommGroup V₁] [inst_2 : Module k V₁] [inst_3 : AddTorsor V₁ P₁]
  [inst_4 : TopologicalSpace P₁] [inst_5 : AddCommGroup V₂] [inst_6 : Module k V₂] [inst_7 : AddTorsor V₂ P₂]
  [inst_8 : TopologicalSpace P₂] [inst_9 : AddCommGroup V₃] [inst_10 : Module k V₃] [inst_11 : AddTorsor V₃ P₃]
  [inst_12 : TopologicalSpace P₃] [inst_13 : TopologicalSpace V₁] [inst_14 : IsTopologicalAddTorsor P₁]
  [inst_15 : TopologicalSpace V₂] [inst_16 : IsTopologicalAddTorsor P₂] [inst_17 : TopologicalSpace V₃]
  [inst_18 : IsTopologicalAddTorsor P₃] (f : P₁ →ᴬ[k] P₂) (g : P₁ →ᴬ[k] P₃),
  (f.prod g).contLinear = f.contLinear.prod g.contLinear