{𝕜 : Type u_6} →
  {𝕜' : Type u_7} →
    [inst : NormedField 𝕜] →
      [inst_1 : SeminormedRing 𝕜'] →
        (smul : 𝕜 → 𝕜' → 𝕜') →
          (algebraMap : 𝕜 →+* 𝕜') →
            (∀ (r : 𝕜) (x : 𝕜'), algebraMap r * x = x * algebraMap r) →
              (∀ (r : 𝕜) (x : 𝕜'), r • x = algebraMap r * x) →
                (∀ (r : 𝕜) (x : 𝕜'), ‖r • x‖ ≤ ‖r‖ * ‖x‖) → NormedAlgebra 𝕜 𝕜'