Theorems · Theorem · order theory
Set.IsWF.isPWO
∀ {α : Type u_2} [inst : LinearOrder α] {s : Set α}, s.IsWF → s.IsPWOAlias of the reverse direction of Set.isPWO_iff_isWF.
In a linear order, the predicates Set.IsPWO and Set.IsWF are equivalent.
- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LinearOrderstatement and proof · cited by 8,572
- Set.IsPWOstatement · cited by 99
- Set.IsWFstatement · cited by 47
- Set.isPWO_iff_isWFproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- Set.IsWF.vaddproof · cited by 2
- Finset.vaddAntidiagonal_min_vadd_minstatement and proof · cited by 1
- Set.IsWF.mulproof · cited by 1
- Set.IsWF.smulproof · cited by 1
- Set.IsWF.addproof · cited by 1
- Finset.antidiagonal_min_add_minstatement · cited by 1
- HahnSeries.suppBddBelow_supp_PWOproof · cited by 0
- Set.MulAntidiagonal.finite_of_isWFproof · cited by 0
- Set.AddAntidiagonal.finite_of_isWFproof · cited by 0
- Finset.addAntidiagonal_min_mul_minstatement · cited by 0
- Set.IsPWO.of_linearOrderproof · cited by 0
- Finset.smulAntidiagonal_min_smul_minstatement and proof · cited by 0