Theorems · Theorem · logic and foundations
Cardinal.preBeth_omega
Cardinal.preBeth Ordinal.omega0 = Cardinal.aleph0
- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- le_antisymmproof · cited by 2,068
- Ordinalproof · cited by 1,688
- Set.Iioproof · cited by 1,166
- Cardinal.aleph0statement and proof · cited by 521
- Ordinal.omega0statement and proof · cited by 197
- Cardinal.bddAbove_of_smallproof · cited by 37
- Order.IsSuccLimit.isSuccPrelimitproof · cited by 37
- Cardinal.preBethstatement and proof · cited by 31
- Cardinal.natCast_le_aleph0proof · cited by 20
- Ordinal.lt_omega0proof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.beth_zeroproof · cited by 1