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