Theorems · Theorem · logic and foundations
Cardinal.aleph_lt_aleph
∀ {o₁ o₂ : Ordinal.{u_1}}, Cardinal.aleph o₁ < Cardinal.aleph o₂ ↔ o₁ < o₂- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 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
- OrderEmbeddingstatement · cited by 619
- Cardinal.alephstatement and proof · cited by 76
- OrderEmbedding.lt_iff_ltproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_opow_omegaproof · cited by 2
- Cardinal.aleph0_lt_alephproof · cited by 0