Theorems · Theorem · logic and foundations
Cardinal.aleph0_le
∀ {c : Cardinal.{u_1}}, Cardinal.aleph0 ≤ c ↔ ∀ (n : ℕ), ↑n ≤ c- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- Cardinal.aleph0statement and proof · cited by 521
- le_of_not_gtproof · cited by 430
- LT.lt.not_geproof · cited by 305
- Nat.cast_leproof · cited by 159
- Cardinal.natCast_le_aleph0proof · cited by 20
- Cardinal.lt_aleph0proof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- aleph0_le_rank_of_isEmpty_oreSetproof · cited by 1
- Cardinal.toNat_eq_of_forall_le_iffproof · cited by 1