Theorems · Theorem · order theory
Order.krullDim_eq_length_of_finiteDimensionalOrder
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : FiniteDimensionalOrder α],
Order.krullDim α = ↑(LTSeries.longestOf α).length- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Set.ofPredstatement and proof · cited by 6,101
- ENatstatement · cited by 4,985
- le_antisymmproof · cited by 2,068
- WithBotstatement · cited by 1,498
- le_iSupproof · cited by 207
- RelSeries.lengthstatement and proof · cited by 195
- iSup_leproof · cited by 190
- LTSeriesproof · cited by 87
- Order.krullDimstatement · cited by 82
- WithBot.coe_le_coeproof · cited by 76
- WithTop.coe_le_coeproof · cited by 65
Cited by3
Results whose statement or proof uses this declaration.
- Order.krullDim_eq_top_iffproof · cited by 1
- LTSeries.height_last_longestOfproof · cited by 1
- Order.le_krullDim_iffproof · cited by 0