localization_mul — Mathlib

English

Localization commutes with multiplication: (r ⋅ s).localization L W = r.localization L W ⋅ s.localization L W.

Русский

Локализация сохраняет умножение: (r ⋅ s).localization = r.localization ⋅ s.localization.

LaTeX

$$$ (r * s).localization\; L\; W = r.localization\; L\; W * s.localization\; L\; W$$$

Lean4

theorem localization_mul : (r * s).localization L W = r.localization L W * s.localization L W :=
  ext_of_localization L W _ _ (fun X => by simp)

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