Theorems · Theorem · logic and foundations
ZFSet.rank_eq_wfRank
∀ {x : ZFSet.{u}}, Ordinal.lift.{u + 1, u} x.rank = IsWellFounded.rank (fun x1 x2 => x1 ∈ x2) xZFSet.rank is equal to the IsWellFounded.rank over ∈.
- Defined in
- Mathlib.SetTheory.ZFC.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupproof · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- Order.succproof · cited by 633
- LE.le.antisymmproof · cited by 507
- ZFSetstatement and proof · cited by 259
- Order.succ_eq_add_oneproof · cited by 115
- Ordinal.liftstatement and proof · cited by 86
- ZFSet.rankstatement and proof · cited by 31
- le_of_forall_ltproof · cited by 25
- Ordinal.iSup_leproof · cited by 18
- IsWellFounded.rankstatement and proof · cited by 9
- ZFSet.rank_lt_of_memproof · cited by 8
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