star_algebraMap — Mathlib

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]

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