Theorems · Theorem · logic and foundations
Cardinal.aleph0_le_aleph
∀ (o : Ordinal.{u_1}), Cardinal.aleph0 ≤ Cardinal.aleph o- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 9 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.
Cites9
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 and proof · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- OrderEmbeddingstatement · cited by 619
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.alephstatement · cited by 76
- le_self_addproof · cited by 68
- Cardinal.aleph_eq_preAlephproof · cited by 4
- Cardinal.aleph0_le_preAlephproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- Cardinal.isRegular_aleph_add_oneproof · cited by 2
- Cardinal.isSuccLimit_omegaproof · cited by 2
- Cardinal.range_alephproof · cited by 1
- Cardinal.aleph0_le_bethproof · cited by 1
- Cardinal.aleph_mul_alephproof · cited by 0
- Cardinal.aleph_posproof · cited by 0
- Cardinal.aleph_toENatproof · cited by 0
- Cardinal.aleph_toNatproof · cited by 0
- Cardinal.aleph_add_alephproof · cited by 0