Theorems · Theorem · logic and foundations
Cardinal.ord_preAleph
∀ (o : Ordinal.{u_1}), (Cardinal.preAleph o).ord = Ordinal.preOmega o- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 91 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 and proof · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- OrderIsostatement · cited by 874
- OrderEmbeddingstatement · cited by 619
- Cardinal.ordstatement and proof · cited by 266
- Cardinal.preAlephstatement · cited by 44
- Ordinal.preOmegastatement and proof · cited by 31
- Ordinal.card_preOmegaproof · cited by 4
- Ordinal.IsInitial.ord_cardproof · cited by 4
- Ordinal.isInitial_preOmegaproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.ord_alephproof · cited by 7
- Ordinal.lift_preOmegaproof · cited by 1
- Cardinal.IsInaccessible.preOmega_ordproof · cited by 1
- Cardinal.cof_preOmega_add_oneproof · cited by 0
- Cardinal.preAleph_of_omega0_sq_leproof · cited by 0