Theorems · Theorem · logic and foundations
ZFSet.rank_sUnion_le
∀ (x : ZFSet.{u_1}), x.sUnion.rank ≤ x.rankFor the rank of ⋃₀ x, we only have rank (⋃₀ x) ≤ rank x ≤ rank (⋃₀ x) + 1.
This inequality is split into rank_sUnion_le and le_succ_rank_sUnion.
- Defined in
- Mathlib.SetTheory.ZFC.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement · cited by 1,688
- ZFSetstatement and proof · cited by 259
- ZFSet.rankstatement and proof · cited by 31
- ZFSet.sUnionstatement · cited by 15
- ZFSet.rank_lt_of_memproof · cited by 8
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