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]