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Theorems · Theorem · order theory

Set.isPWO_iff_isWF

∀ {α : Type u_2} [inst : LinearOrder α] {s : Set α}, s.IsPWO ↔ s.IsWF

In a linear order, the predicates Set.IsPWO and Set.IsWF are equivalent.

Defined in
Mathlib.Order.WellFoundedSet
Cited by
1 results in Mathlib
Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.IsWF.isPWO · cited by 13IsWF.isPWOSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.IsPWO · cited by 99Set.IsPWOSet.IsWF · cited by 47Set.IsWFWellQuasiOrderedLE · cited by 22WellQuasiOrderedLEIsWellFounded · cited by 18IsWellFoundedisWellFounded_iff · cited by 9isWellFounded_iffwellQuasiOrderedLE_def · cited by 2wellQuasiOrderedLE_defwellQuasiOrderedLE_iff_wellFoundedLT · cited by 1wellQuasiOrderedLE_iff_we…Set.isPWO_iff_isWFCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.