Theorems · Theorem · order theory
Order.krullDim_eq_bot
∀ {α : Type u_1} [inst : Preorder α] [IsEmpty α], Order.krullDim α = ⊥- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Bot.botstatement · cited by 4,720
- WithBotstatement · cited by 1,498
- IsEmptystatement and proof · cited by 759
- Order.krullDimstatement · cited by 82
- Order.krullDim_eq_bot_iffproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- ringKrullDim_eq_bot_of_subsingletonproof · cited by 5
- Order.krullDim_eq_iSup_heightproof · cited by 3
- Order.krullDim_eq_top_iffproof · cited by 1
- Order.krullDim_eq_iSup_coheightproof · cited by 1
- Order.le_krullDim_iffproof · cited by 0