∀ {K : Type u} [inst : NontriviallyNormedField K] {L : Type v} [inst_1 : Field L] [inst_2 : Algebra K L]
  [Algebra.IsAlgebraic K L] [hu : IsUltrametricDist K] [CompleteSpace K] {f : AbsoluteValue L ℝ},
  (∀ (x : K), f ((algebraMap K L) x) = ‖x‖) → ∀ (x : L), f x = spectralNorm K L x