Mathlib Map

Theorems · Theorem · logic and foundations

IsWellFounded.rank_eq

∀ {α : Type u} (r : α → α → Prop) [hwf : IsWellFounded α r] (a : α),
  IsWellFounded.rank r a = ⨆ b, Order.succ (IsWellFounded.rank r ↑b)
Defined in
Mathlib.SetTheory.Ordinal.Rank
Cited by
2 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IsWellFounded
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

PSet.rank_eq_wfRank · cited by 0PSet.rank_eq_wfRankZFSet.rank_eq_wfRank · cited by 0ZFSet.rank_eq_wfRankiSup · cited by 2415iSupOrdinal · cited by 1688OrdinalOrder.succ · cited by 633Order.succIsWellFounded · cited by 18IsWellFoundedIsWellFounded.rank · cited by 9IsWellFounded.rankIsWellFounded.apply · cited by 5IsWellFounded.applyAcc.rank_eq · cited by 3Acc.rank_eqIsWellFounded.rank_eqCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.