algNormOfAlgEquiv_extends — Mathlib

English

The algebra norm algNormOfAlgEquiv σ is nonarchimedean.

Русский

Алгебрная норма algNormOfAlgEquiv σ нерarchимедова.

LaTeX

$$IsNonarchimedean (algNormOfAlgEquiv σ)$$

Lean4

/-- The algebra norm `algNormOfAlgEquiv` extends the norm on `K`. -/
theorem algNormOfAlgEquiv_extends (σ : L ≃ₐ[K] L) (x : K) : (algNormOfAlgEquiv σ) ((algebraMap K L) x) = ‖x‖ :=
  by
  simp only [algNormOfAlgEquiv_apply, AlgEquiv.commutes]
  exact
    (Classical.choose_spec
            (exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional h_fin hu.isNonarchimedean_norm)).2.1
      _

Похожие утверждения