Theorems · Theorem · order theory
Order.krullDimLE_iff
∀ (n : ℕ) (α : Type u_1) [inst : Preorder α], Order.KrullDimLE n α ↔ Order.krullDim α ≤ ↑n
- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- ENatstatement · cited by 4,985
- WithBotstatement · cited by 1,498
- Order.krullDimstatement and proof · cited by 82
- Order.KrullDimLEstatement and proof · cited by 3
- Order.KrullDimLE.casesOnproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Ring.krullDimLE_iffproof · cited by 5
- AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zeroproof · cited by 2
- ringKrullDimZero_iff_ringKrullDim_eq_zeroproof · cited by 1
- isFiniteLength_quotient_span_singletonproof · cited by 1