Instances for Euclidean domains

• Int.euclideanDomain: shows that ℤ is a Euclidean domain.
• Field.toEuclideanDomain: shows that any field is a Euclidean domain.

instance Int.euclideanDomain : EuclideanDomain ℤ

Equations

• One or more equations did not get rendered due to their size.

@[instance 100]

instance Field.toEuclideanDomain {K : Type u_1} [Field K] : EuclideanDomain K

Equations

• Field.toEuclideanDomain = EuclideanDomain.mk (fun (x x_1 : K) => x / x_1) ⋯ (fun (a b : K) => a - a * b / b) ⋯ (fun (a b : K) => a = 0 ∧ b ≠ 0) ⋯ ⋯ ⋯