Theorems · Theorem · order theory
Order.coheight_of_noMaxOrder
∀ {α : Type u_1} [inst : Preorder α] [NoMaxOrder α] (a : α), Order.coheight a = ⊤- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNoMaxOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- ENatstatement · cited by 4,985
- Set.Ioiproof · cited by 1,463
- StrictMonoproof · cited by 706
- Subtype.propproof · cited by 505
- NoMaxOrderstatement and proof · cited by 340
- Order.coheightstatement · cited by 74
- Nat.exists_strictMonoproof · cited by 2
- Order.coheight_eq_top_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Order.krullDim_of_noMaxOrderproof · cited by 3
- Order.height_of_noMinOrderproof · cited by 2
- Order.coheight_natproof · cited by 1
- Order.coheight_intproof · cited by 0