embed_product_star — Mathlib

English

The star operation commutes with embedding from Units into the product: embedProduct of star u equals star of embedProduct u.

Русский

Звезда commuting с вложением из единиц в произведение: embedProduct R (star u) = star (embedProduct R u).

LaTeX

$$$\\\\mathrm{Units.embedProduct}_R(\\\\star u) = \\\\star\\\\bigl(\\\\mathrm{Units.embedProduct}_R(u)\\\\bigr).$$$

Lean4

theorem embed_product_star [Monoid R] [StarMul R] (u : Rˣ) :
    Units.embedProduct R (star u) = star (Units.embedProduct R u) :=
  rfl

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