Theorems · Theorem · logic and foundations
Cardinal.ord_aleph
∀ (o : Ordinal.{u_1}), (Cardinal.aleph o).ord = Ordinal.omega o- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Cardinalstatement · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- OrderEmbeddingstatement · cited by 619
- Cardinal.ordstatement · cited by 266
- Ordinal.omega0proof · cited by 197
- Cardinal.alephstatement · cited by 76
- Ordinal.omegastatement · cited by 60
- RelEmbedding.toEmbeddingproof · cited by 45
- OrderEmbedding.addLeftproof · cited by 5
- Cardinal.ord_preAlephproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Cardinal.IsRegular.cof_omega_eqproof · cited by 2
- Cardinal.isSingular_aleph_iffproof · cited by 2
- Cardinal.isSuccLimit_omegaproof · cited by 2
- MeasurableSpace.cardinal_generateMeasurableRec_leproof · cited by 1
- Cardinal.IsInaccessible.omega_ordproof · cited by 1
- Ordinal.cof_eq_aleph0_of_isSuccLimitproof · cited by 1
- Cardinal.preAleph_of_omega0_sq_leproof · cited by 0