mapPosSubmonoid — Mathlib

English

The map on posSubmonoid induced by an algebra map sends ⟨r,s⟩ to ⟨algebraMap r, mapPosSubmonoid s⟩.

Русский

Отображение на подпмножествах позитронного подпорядка, индуцированное алгебраической картой, отправляет ⟨r,s⟩ в ⟨algebraMap r, mapPosSubmonoid s⟩.

LaTeX

$$$\\text{mapPosSubmonoid}(A,B)(\\langle r, s \\rangle) = \\langle \\mathrm{algebraMap}(A,B)(r), \\mathrm{mapPosSubmonoid}(A,B)(s) \\rangle$$$

Lean4

/-- The morphism of `posSubmonoid`s associated to an algebra map.
  This is used in constructing `ValuativeExtension.mapValueGroupWithZero`. -/
@[simps]
def mapPosSubmonoid : posSubmonoid A →* posSubmonoid B
    where
  toFun := fun ⟨a, ha⟩ =>
    ⟨algebraMap _ _ a, by simpa only [posSubmonoid_def, ← (algebraMap A B).map_zero, srel_iff_srel] using ha⟩
  map_one' := by simp
  map_mul' := by simp

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