Theorems · Theorem · logic and foundations
Cardinal.mk_toNat_eq_card
∀ {α : Type u} [inst : Fintype α], Cardinal.toNat (Cardinal.mk α) = Fintype.card α- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Fintypestatement and proof · cited by 7,736
- Cardinalstatement · cited by 2,598
- Fintype.cardstatement and proof · cited by 1,386
- Cardinal.mkstatement · cited by 942
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.toNatstatement and proof · cited by 153
- Cardinal.mk_fintypeproof · cited by 81
- Cardinal.toNat_natCastproof · cited by 19
Cited by6
Results whose statement or proof uses this declaration.
- Nat.card_eq_fintype_cardproof · cited by 200
- Fintype.card_eq_nat_cardproof · cited by 31
- Module.finrank_pi_fintypeproof · cited by 6
- Module.finrank_finsupp_selfproof · cited by 3
- Module.finrank_directSumproof · cited by 2
- Module.finrank_finsuppproof · cited by 0