∀ {k : Type u_1} {P₁ : Type u_2} {P₂ : Type u_3} {V₁ : Type u_4} {V₂ : Type u_5} {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}
  {toAffineEquiv : P₁ ≃ᵃ[k] P₂}
  {continuous_toFun : autoParam (Continuous toAffineEquiv.toFun) ContinuousAffineEquiv.continuous_toFun._autoParam}
  {continuous_invFun : autoParam (Continuous toAffineEquiv.invFun) ContinuousAffineEquiv.continuous_invFun._autoParam}
  {toAffineEquiv_1 : P₁ ≃ᵃ[k] P₂}
  {continuous_toFun_1 : autoParam (Continuous toAffineEquiv_1.toFun) ContinuousAffineEquiv.continuous_toFun._autoParam}
  {continuous_invFun_1 :
    autoParam (Continuous toAffineEquiv_1.invFun) ContinuousAffineEquiv.continuous_invFun._autoParam},
  { toAffineEquiv := toAffineEquiv, continuous_toFun := continuous_toFun, continuous_invFun := continuous_invFun } =
      { toAffineEquiv := toAffineEquiv_1, continuous_toFun := continuous_toFun_1,
        continuous_invFun := continuous_invFun_1 } →
    toAffineEquiv = toAffineEquiv_1