mapValueGroupWithZero_mk — Mathlib

English

For any field K with a valuative relation, valuation K is surjective onto ValueGroupWithZero K.

Русский

Для любой поля K с валюативным отношением отображение valuation surjective на ValueGroupWithZero K.

LaTeX

$$$\\text{Valuation}_{K} : K \\to \\mathrm{ValueGroupWithZero} K$ is surjective$$

Lean4

@[simp]
theorem mapValueGroupWithZero_mk (r : A) (s : posSubmonoid A) :
    mapValueGroupWithZero A B (.mk r s) = .mk (algebraMap A B r) (mapPosSubmonoid A B s) := by
  simp [mapValueGroupWithZero, ValueGroupWithZero.mk_eq_div (R := B)]

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