Theorems · Definition · logic and foundations
Cardinal.toNat
Cardinal.{u_1} →*₀ ℕThis function sends finite cardinals to the corresponding natural, and infinite cardinals to 0.
- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 153 results in Mathlib
- Foundations
- Depth 88 from the axioms, rests on 2,427 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- MonoidWithZeroHomstatement · cited by 704
- MonoidWithZeroHom.ofClassproof · cited by 204
- Cardinal.toENatproof · cited by 92
- MonoidWithZeroHom.compproof · cited by 34
- ENat.toNatHomproof · cited by 3
Cited by156
Results whose statement or proof uses this declaration.
- Module.finrankproof · cited by 1,770
- Nat.cardproof · cited by 844
- LinearEquiv.finrank_eqproof · cited by 65
- Submodule.spanFinrankproof · cited by 49
- Cardinal.toNat_liftstatement · cited by 41
- finrank_topproof · cited by 31
- Module.finrank_mul_finrankproof · cited by 26
- Nat.card_prodproof · cited by 24
- Module.finrank_eq_card_chooseBasisIndexproof · cited by 21
- Cardinal.toNat_natCaststatement · cited by 19
- Cardinal.toNat_le_toNatstatement · cited by 14
- Module.finrank_eq_of_rank_eqproof · cited by 13