Theorems · Theorem · logic and foundations
Cardinal.succ_aleph
∀ (o : Ordinal.{u_1}), Order.succ (Cardinal.aleph o) = Cardinal.aleph (o + 1)- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 4 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 and proof · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- add_assocproof · cited by 746
- Order.succstatement and proof · cited by 633
- OrderEmbeddingstatement · cited by 619
- Ordinal.omega0proof · cited by 197
- Cardinal.alephstatement and proof · cited by 76
- Cardinal.preAlephproof · cited by 44
- Cardinal.aleph_eq_preAlephproof · cited by 4
- Cardinal.succ_preAlephproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Cardinal.succ_aleph0proof · cited by 6
- Cardinal.isRegular_aleph_add_oneproof · cited by 2
- Cardinal.aleph_succproof · cited by 0
- Cardinal.aleph_add_oneproof · cited by 0