Theorems · Theorem · logic and foundations
Cardinal.toNat_eq_iff
∀ {c : Cardinal.{u}} {n : ℕ}, n ≠ 0 → (Cardinal.toNat c = n ↔ c = ↑n)- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.toNatstatement · cited by 153
- Cardinal.toENat_eq_natCastproof · cited by 6
- ENat.toNat_eq_iffproof · cited by 4
- Cardinal.toNat_toENatproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.toNat_eq_oneproof · cited by 4
- Cardinal.toNat_eq_ofNatproof · cited by 3
- finrank_eq_one_iff'proof · cited by 2
- Subalgebra.finrank_eq_one_iffproof · cited by 2
- Field.Emb.cardinal_eq_of_isSeparableproof · cited by 1