norm_def' — Mathlib

English

expMapBasis is injective as a map from realSpace K to realSpace K.

Русский

expMapBasis инъективно.

LaTeX

$$$\text{Injective}(\expMapBasis : \mathbb{R}^{r} \to \mathbb{R}^{r})$$$

Lean4

/-- The norm of the image after the embedding associated to `v` is equal to the norm of `v` raised
to the power of the `v`-adic valuation. -/
theorem norm_def' (x : WithVal (v.valuation K)) : ‖embedding v x‖ = toNNReal (absNorm_ne_zero v) (v.valuation K x) := by
  rw [norm_def, adicAbv_def]

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