{𝕜 : Type u_1} →
  {𝕜₂ : Type u_2} →
    {E : Type u_4} →
      {F : Type u_5} →
        [inst : SeminormedAddCommGroup E] →
          [inst_1 : SeminormedAddCommGroup F] →
            [inst_2 : NontriviallyNormedField 𝕜] →
              [inst_3 : NontriviallyNormedField 𝕜₂] →
                [inst_4 : NormedSpace 𝕜 E] →
                  [inst_5 : NormedSpace 𝕜₂ F] →
                    {σ₁₂ : 𝕜 →+* 𝕜₂} → [RingHomIsometric σ₁₂] → PseudoMetricSpace (E →SL[σ₁₂] F)