English
For indexed families of rings, the symmetry of the product-level ring isomorphism piCongrRight is componentwise symmetric: (piCongrRight e).symm = piCongrRight i (e i).symm.
Русский
Для индексированных семейств колец их симметричный произведениеобразий, пирингравитное, имеет компонентную симм: (piCongrRight e).symm = piCongrRight i (e i).symm.
LaTeX
$$$\\big( \\mathrm{piCongrRight} \\, e \\big)^{\\,-1} = \\mathrm{piCongrRight} (\\lambda i, e(i)^{-1})$$$
Lean4
@[simp]
theorem piCongrRight_symm {ι : Type*} {R S : ι → Type*} [∀ i, NonUnitalNonAssocSemiring (R i)]
[∀ i, NonUnitalNonAssocSemiring (S i)] (e : ∀ i, R i ≃+* S i) :
(piCongrRight e).symm = piCongrRight fun i => (e i).symm :=
rfl
