Theorems · Theorem · logic and foundations
Cardinal.toNat_eq_ofNat
∀ {c : Cardinal.{u}} {n : ℕ} [inst : n.AtLeastTwo], Cardinal.toNat c = OfNat.ofNat n ↔ c = OfNat.ofNat nA version of toNat_eq_iff for literals
- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nat.AtLeastTwo
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
- Nat.AtLeastTwostatement and proof · cited by 405
- Cardinal.toNatstatement · cited by 153
- OfNat.ofNat_ne_zeroproof · cited by 20
- Cardinal.toNat_eq_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Nat.card_eq_two_iff'proof · cited by 4
- Nat.card_eq_two_iffproof · cited by 1
- Module.rank_eq_ofNat_iff_finrank_eq_ofNatproof · cited by 0