Theorems · Theorem · logic and foundations
Cardinal.succ_aleph0
Order.succ Cardinal.aleph0 = Cardinal.aleph 1
- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- zero_addproof · cited by 2,366
- Ordinalstatement and proof · cited by 1,688
- Order.succstatement and proof · cited by 633
- OrderEmbeddingstatement · cited by 619
- Cardinal.aleph0statement · cited by 521
- Cardinal.alephstatement and proof · cited by 76
- Cardinal.succ_alephproof · cited by 4
- Cardinal.aleph_zeroproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Cardinal.lt_aleph_one_iffproof · cited by 3
- Cardinal.isRegular_aleph_oneproof · cited by 3
- Cardinal.aleph_one_le_iffproof · cited by 2
- Ordinal.cof_eq_aleph0_of_isSuccLimitproof · cited by 1
- Cardinal.aleph_one_le_continuumproof · cited by 1
- Cardinal.exists_uncountable_fiberproof · cited by 0