theorem thm51_dim_affine_space (k : Type u_1) [Field k] (n : ℕ) : ringKrullDim (MvPolynomial (Fin n) k) = ↑n

Lecture 5, Theorem 5.1: affine n-space has dimension n, i.e. dim k[x_1, …, x_n] = n.

theorem cor11_variety_finite_dim (k : Type u_1) [Field k] (A : Type u_2) [CommRing A] [Algebra k A] [Algebra.FiniteType k A] : ringKrullDim A < ⊤

Lecture 5, Corollary 11: any algebraic variety over a field is finite-dimensional, since any finitely generated k-algebra has finite Krull dimension.