Theorems · Theorem · order theory
Order.krullDim_eq_one_iff_of_boundedOrder
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : BoundedOrder α], Order.krullDim α = 1 ↔ IsSimpleOrder α- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderBoundedOrder
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.
- Top.topproof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- ENatstatement · cited by 4,985
- Bot.botproof · cited by 4,720
- Nontrivialproof · cited by 2,416
- WithBotstatement · cited by 1,498
- BoundedOrderstatement and proof · cited by 270
- Order.krullDimstatement and proof · cited by 82
- le_antisymm_iffproof · cited by 62
- IsSimpleOrderstatement and proof · cited by 54
- Order.krullDim_le_one_iff_of_boundedOrderproof · cited by 2
- WithBot.one_le_iff_posproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Module.length_eq_one_iffproof · cited by 4
- Order.krullDim_of_isSimpleOrderproof · cited by 0