Theorems · Definition · order theory
Set.IsPWO
{α : Type u_2} → [Preorder α] → Set α → PropA subset of a preorder is partially well-ordered when any infinite sequence contains a monotone subsequence of length 2 (or equivalently, an infinite monotone subsequence).
- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 25 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.PartiallyWellOrderedOnproof · cited by 34
Cited by113
Results whose statement or proof uses this declaration.
- HahnSeries.extproof · cited by 53
- Finset.antidiagonalstatement and proof · cited by 23
- HahnSeries.isPWO_supportstatement · cited by 20
- Set.VAddAntidiagonal.finite_of_isPWOstatement and proof · cited by 16
- Set.IsWF.isPWOstatement · cited by 13
- Set.IsPWO.monostatement and proof · cited by 11
- Set.IsPWO.isWFstatement and proof · cited by 9
- Finset.mulAntidiagonalstatement and proof · cited by 8
- HahnSeries.isPWO_support'statement · cited by 6
- Set.IsPWO.image_of_monotonestatement and proof · cited by 5
- Finset.mem_antidiagonalstatement and proof · cited by 5
- Set.Finite.isPWOstatement · cited by 5