Theorems · Theorem · order theory
Order.height_eq_krullDim_Iic
∀ {α : Type u_1} [inst : Preorder α] (x : α), ↑(Order.height x) = Order.krullDim ↑(Set.Iic x)- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 2 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.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topproof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- Set.Elemstatement and proof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- iSupproof · cited by 2,415
- le_antisymmproof · cited by 2,068
- WithBotstatement and proof · cited by 1,498
- Set.Iicstatement and proof · cited by 1,111
- le_transproof · cited by 985
- StrictMonoproof · cited by 706
- WithBot.somestatement and proof · cited by 541
Cited by2
Results whose statement or proof uses this declaration.
- Module.length_submoduleproof · cited by 2
- Order.coheight_eq_krullDim_Iciproof · cited by 1