Theorems · Theorem · order theory
Order.height_top_eq_krullDim
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : OrderTop α], ↑(Order.height ⊤) = Order.krullDim α- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- ENatstatement and proof · cited by 4,985
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- WithBotstatement and proof · cited by 1,498
- WithBot.somestatement and proof · cited by 541
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- iSup_leproof · cited by 190
- RelSeries.lastproof · cited by 114
- LTSeriesproof · cited by 87
Cited by6
Results whose statement or proof uses this declaration.
- IsLocalRing.maximalIdeal_height_eq_ringKrullDimproof · cited by 4
- Order.height_eq_krullDim_Iicproof · cited by 2
- Order.krullDim_WithTopproof · cited by 2
- Order.coheight_bot_eq_krullDimproof · cited by 2
- Order.height_enatproof · cited by 1
- Module.length_eq_heightproof · cited by 1