Theorems · Theorem · logic and foundations
Cardinal.aleph_le_beth
∀ (o : Ordinal.{u_1}), Cardinal.aleph o ≤ Cardinal.beth o- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 3 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.
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 · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- OrderEmbeddingstatement · cited by 619
- Ordinal.omega0proof · cited by 197
- Cardinal.alephstatement · cited by 76
- RelEmbedding.toEmbeddingproof · cited by 45
- Cardinal.bethstatement · cited by 35
- OrderEmbedding.addLeftproof · cited by 5
- Cardinal.preAleph_le_preBethproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.IsInaccessible.aleph_ordproof · cited by 2
- Ordinal.card_le_bethproof · cited by 1
- Cardinal.aleph0_le_bethproof · cited by 1