Theorems · Theorem · logic and foundations
Cardinal.aleph0_le_preAleph
∀ {o : Ordinal.{u_1}}, Cardinal.aleph0 ≤ Cardinal.preAleph o ↔ Ordinal.omega0 ≤ o- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 3 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.
Cites9
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
- Cardinal.aleph0statement · cited by 521
- Ordinal.omega0statement and proof · cited by 197
- Cardinal.preAlephstatement and proof · cited by 44
- Cardinal.preAleph_omega0proof · cited by 4
- Cardinal.preAleph_le_preAlephproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.aleph0_le_alephproof · cited by 9
- Cardinal.isRegular_preAleph_add_oneproof · cited by 2
- Cardinal.range_alephproof · cited by 1