Theorems · Theorem · logic and foundations
Cardinal.toNat_eq_one
∀ {c : Cardinal.{u}}, Cardinal.toNat c = 1 ↔ c = 1- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 91 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
- Nat.cast_oneproof · cited by 2,501
- one_ne_zeroproof · cited by 885
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.toNatstatement · cited by 153
- Cardinal.toNat_eq_iffproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Module.rank_eq_one_iff_finrank_eq_oneproof · cited by 8
- Subalgebra.eq_bot_of_finrank_oneproof · cited by 3
- Subfield.relfinrank_eq_one_iffproof · cited by 2
- Cardinal.toNat_eq_one_iff_uniqueproof · cited by 1