{R₁ : Type u_1} →
  {R₂ : Type u_2} →
    [inst : Semiring R₁] →
      [inst_1 : Semiring R₂] →
        {σ₁₂ : R₁ →+* R₂} →
          {σ₂₁ : R₂ →+* R₁} →
            [inst_2 : RingHomInvPair σ₁₂ σ₂₁] →
              [inst_3 : RingHomInvPair σ₂₁ σ₁₂] →
                {M₁ : Type u_4} →
                  [inst_4 : TopologicalSpace M₁] →
                    [inst_5 : AddCommMonoid M₁] →
                      {M₂ : Type u_5} →
                        [inst_6 : TopologicalSpace M₂] →
                          [inst_7 : AddCommMonoid M₂] →
                            [inst_8 : Module R₁ M₁] →
                              [inst_9 : Module R₂ M₂] →
                                (f₁ : M₁ →SL[σ₁₂] M₂) →
                                  (f₂ : M₂ →SL[σ₂₁] M₁) →
                                    f₁.comp f₂ = ContinuousLinearMap.id R₂ M₂ →
                                      f₂.comp f₁ = ContinuousLinearMap.id R₁ M₁ → M₁ ≃SL[σ₁₂] M₂