diff --git a/CommAlg/sayantan(poly_over_field).lean b/CommAlg/sayantan(poly_over_field).lean index fc5f967..48aa955 100644 --- a/CommAlg/sayantan(poly_over_field).lean +++ b/CommAlg/sayantan(poly_over_field).lean @@ -7,7 +7,7 @@ import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic namespace Ideal -private lemma singleton_chainHeight_one {α : Type} [Preorder α] [Bot α] : Set.chainHeight {(⊥ : α)} ≤ 1 := by +private lemma singleton_bot_chainHeight_one {α : Type} [Preorder α] [Bot α] : Set.chainHeight {(⊥ : α)} ≤ 1 := by unfold Set.chainHeight simp only [iSup_le_iff, Nat.cast_le_one] intro L h @@ -67,7 +67,7 @@ lemma polynomial_over_field_dim_one {K : Type} [Nontrivial K] [Field K] : krullD unfold height rw [sngletn] simp only [WithBot.coe_le_one, ge_iff_le] - exact singleton_chainHeight_one + exact singleton_bot_chainHeight_one · suffices : ∃I : PrimeSpectrum (Polynomial K), 1 ≤ (height I : WithBot ℕ∞) · obtain ⟨I, h⟩ := this have : (height I : WithBot ℕ∞) ≤ ⨆ (I : PrimeSpectrum (Polynomial K)), ↑(height I) := by