Theorems · Theorem · order theory
Order.finiteDimensionalOrder_iff_krullDim_ne_bot_and_top
∀ {α : Type u_1} [inst : Preorder α], FiniteDimensionalOrder α ↔ Order.krullDim α ≠ ⊥ ∧ Order.krullDim α ≠ ⊤- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 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.
Cites10
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 · cited by 4,985
- Bot.botstatement and proof · cited by 4,720
- WithBotstatement · cited by 1,498
- Order.krullDimstatement and proof · cited by 82
- not_nonempty_iffproof · cited by 20
- FiniteDimensionalOrderstatement and proof · cited by 17
- Order.krullDim_eq_bot_iffproof · cited by 4
- LTSeries.nonempty_of_finiteDimensionalOrderproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Order.krullDim_ne_top_of_finiteDimensionalOrderproof · cited by 2
- Order.krullDim_ne_bot_of_finiteDimensionalOrderproof · cited by 1
- finiteRingKrullDim_iff_ne_bot_and_topproof · cited by 0