algebra — Mathlib

English

Duplicate of the symmetry application for the right component of the sum-arrow to prod-arrow equivalence.

Русский

Дубликат применения симметрии к правому компоненту эквивалентности sumArrowEquivProdArrow.

LaTeX

$$$$ (\mathrm{sumArrowEquivProdArrow}(α, β, R, S))^{-1} x = (\mathrm{Equiv}.\mathrm{sumArrowEquivProdArrow}(α, β, S))^{-1} x. $$$$

Lean4

instance algebra : Algebra R (A × B)
    where
  algebraMap := RingHom.prod (algebraMap R A) (algebraMap R B)
  commutes' := by
    rintro r ⟨a, b⟩
    dsimp
    rw [commutes r a, commutes r b]
  smul_def' := by
    rintro r ⟨a, b⟩
    dsimp
    rw [Algebra.smul_def r a, Algebra.smul_def r b]

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