Theorems · Theorem · logic and foundations
Cardinal.preAleph_le_preAleph
∀ {o₁ o₂ : Ordinal.{u_1}}, Cardinal.preAleph o₁ ≤ Cardinal.preAleph o₂ ↔ o₁ ≤ o₂- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Cardinalstatement · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- OrderIsostatement · cited by 874
- Cardinal.preAlephstatement and proof · cited by 44
- OrderIso.le_iff_leproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.aleph0_le_preAlephproof · cited by 3
- Cardinal.preAleph_le_alephproof · cited by 1