English
Elements of FiniteAdeleRing are determined by their components, making extensional reasoning valid.
Русский
Элементы FiniteAdeleRing определяются по компонентам, что даёт возможность пользоваться экстенсиональным рассуждением.
LaTeX
$$ext {a1 a2 : IsDedekindDomain.FiniteAdeleRing R K} (h : ∀ v, a1 v = a2 v) : a1 = a2$$
Lean4
/-- A Dedekind domain is an integral domain such that every fractional ideal has an inverse.
This is equivalent to `IsDedekindDomain`.
In particular we provide a `fractional_ideal.comm_group_with_zero` instance,
assuming `IsDedekindDomain A`, which implies `IsDedekindDomainInv`. For **integral** ideals,
`IsDedekindDomain`(`_inv`) implies only `Ideal.cancelCommMonoidWithZero`.
-/
def IsDedekindDomainInv : Prop :=
∀ I ≠ (⊥ : FractionalIdeal A⁰ (FractionRing A)), I * I⁻¹ = 1
