compatible_comap — Mathlib

English

The map on posSubmonoid respects the mk construction: mapPosSubmonoid A B (mk r s) equals mk (algebraMap r) (mapPosSubmonoid s).

Русский

Отображение на подпomонoid сохраняет конструктор mk: mapPosSubmonoid (mk r s) = mk (algebraMap r) (mapPosSubmonoid s).

LaTeX

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

Lean4

instance compatible_comap {Γ : Type*} [LinearOrderedCommMonoidWithZero Γ] (w : Valuation B Γ) [w.Compatible] :
    (w.comap (algebraMap A B)).Compatible := by
  constructor
  simp [← rel_iff_rel (A := A) (B := B), Valuation.Compatible.rel_iff_le (v := w)]

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