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Theorems · Theorem · logic and foundations

ZFSet.rank_le_iff

∀ {x : ZFSet.{u}} {o : Ordinal.{u}}, x.rank ≤ o ↔ ∀ ⦃y : ZFSet.{u}⦄, y ∈ x → y.rank < o
Defined in
Mathlib.SetTheory.ZFC.Rank
Cited by
2 results in Mathlib
Foundations
Depth 85 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_mono · cited by 5ZFSet.rank_monoZFSet.lt_rank_iff · cited by 1ZFSet.lt_rank_iffOrdinal · cited by 1688OrdinalLT.lt.trans_le · cited by 678lt.trans_leZFSet · cited by 259ZFSetPSet · cited by 107PSetZFSet.rank · cited by 31ZFSet.rankZFSet.rank_lt_of_mem · cited by 8ZFSet.rank_lt_of_memPSet.rank_le_iff · cited by 3PSet.rank_le_iffZFSet.rank_le_iffCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.