Theorems · Theorem · order theory
Order.krullDim_eq_iSup_length
∀ {α : Type u_1} [inst : Preorder α] [Nonempty α], Order.krullDim α = ↑(⨆ p, ↑p.length)A definition of krullDim for nonempty α that avoids WithBot
- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 5 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.
Cites14
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 and proof · cited by 4,985
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- WithBotstatement · cited by 1,498
- WithBot.somestatement · cited by 541
- OrderTopproof · cited by 493
- RelSeries.lengthstatement and proof · cited by 195
- SupSetproof · cited by 154
- LTSeriesstatement and proof · cited by 87
- Order.krullDimstatement · cited by 82
Cited by5
Results whose statement or proof uses this declaration.
- Order.height_top_eq_krullDimproof · cited by 6
- Order.height_le_krullDimproof · cited by 5
- ringKrullDim_quotient_succ_le_of_nonZeroDivisorproof · cited by 3
- Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimesproof · cited by 1
- Order.krullDim_eq_iSup_height_add_coheight_of_nonemptyproof · cited by 0