{𝕜 : Type u_6} →
  {𝕜' : Type u_7} →
    {inst : NormedField 𝕜} →
      {inst_1 : SeminormedRing 𝕜'} →
        {P : Sort u} →
          {toAlgebra : Algebra 𝕜 𝕜'} →
            {norm_smul_le : ∀ (r : 𝕜) (x : 𝕜'), ‖r • x‖ ≤ ‖r‖ * ‖x‖} →
              {toAlgebra' : Algebra 𝕜 𝕜'} →
                {norm_smul_le' : ∀ (r : 𝕜) (x : 𝕜'), ‖r • x‖ ≤ ‖r‖ * ‖x‖} →
                  { toAlgebra := toAlgebra, norm_smul_le := norm_smul_le } =
                      { toAlgebra := toAlgebra', norm_smul_le := norm_smul_le' } →
                    (toAlgebra ≍ toAlgebra' → P) → P