English
Star commutes with the algebra map: star(algebraMap_R^(FreeAlgebra) r) = algebraMap_R^(FreeAlgebra) r.
Русский
Звезда commutec с отображением алгебры: star(algebraMap_R^(FreeAlgebra) r) = algebraMap_R^(FreeAlgebra) r.
LaTeX
$$$\operatorname{star}\big(\text{algebraMap}_R(\text{FreeAlgebra}(R,X))(r)\big) = \text{algebraMap}_R(\text{FreeAlgebra}(R,X))\, r$$$
Lean4
@[simp]
theorem star_algebraMap (r : R) : star (algebraMap R (FreeAlgebra R X) r) = algebraMap R _ r := by
simp [star, Star.star]