Mathlib Map

Theorems · Definition · logic and foundations

ZFSet.rank

ZFSet.{u} → Ordinal.{u}

The ordinal rank of a ZFC set

Defined in
Mathlib.SetTheory.ZFC.Rank
Cited by
31 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

ZFSet.rank_lt_of_mem · cited by 8ZFSet.rank_lt_of_memZFSet.rank_mono · cited by 5ZFSet.rank_monoOrdinal.rank_toZFSet · cited by 2Ordinal.rank_toZFSetZFSet.mem_vonNeumann · cited by 2ZFSet.mem_vonNeumannZFSet.rank_insert · cited by 2ZFSet.rank_insertZFSet.rank_le_iff · cited by 2ZFSet.rank_le_iffZFSet.rank_vonNeumann · cited by 2ZFSet.rank_vonNeumannOrdinal.toZFSetIso · cited by 2Ordinal.toZFSetIsoZFSet.subset_vonNeumann · cited by 2ZFSet.subset_vonNeumannZFSet.vonNeumann_add_one · cited by 2ZFSet.vonNeumann_add_oneZFSet.mem_vonNeumann_succ · cited by 1ZFSet.mem_vonNeumann_succZFSet.rank_empty · cited by 1ZFSet.rank_emptyZFSet.rank_powerset · cited by 1ZFSet.rank_powersetZFSet.rank_singleton · cited by 1ZFSet.rank_singletonZFSet.IsOrdinal.rank_inj · cited by 1IsOrdinal.rank_injOrdinal · cited by 1688OrdinalZFSet · cited by 259ZFSetPSet · cited by 107PSetPSet.rank · cited by 16PSet.rankPSet.rank_congr · cited by 2PSet.rank_congrZFSet.rankCITED BYCITES

Cites5

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

Cited by32

Results whose statement or proof uses this declaration.