Theorems · Theorem · logic and foundations
Cardinal.toNat_le_iff_of_lt_aleph0
∀ {a : Cardinal.{u}} (n : ℕ), a < Cardinal.aleph0 → (Cardinal.toNat a ≤ n ↔ a ≤ ↑n)- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 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.
- DFunLike.coestatement and proof · cited by 62,936
- Cardinalstatement and proof · cited by 2,598
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.toNatstatement and proof · cited by 153
- Cardinal.natCast_lt_aleph0proof · cited by 47
- Cardinal.toNat_natCastproof · cited by 19
- Cardinal.toNat_le_iff_le_of_lt_aleph0proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.FG.spanRank_le_iffproof · cited by 2