Theorems · Theorem · logic and foundations
Nat.card_eq_fintype_card
∀ {α : Type u_1} [inst : Fintype α], Nat.card α = Fintype.card α- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 200 results in Mathlib
- Foundations
- Depth 92 from the axioms, rests on 2,429 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement · cited by 1,386
- Nat.cardstatement · cited by 844
- Cardinal.mk_toNat_eq_cardproof · cited by 6
Cited by200
Results whose statement or proof uses this declaration.
- Set.ncard_eq_toFinset_cardproof · cited by 21
- orderOf_dvd_natCardproof · cited by 14
- Nat.card_zmodproof · cited by 13
- Finite.one_lt_card_iff_nontrivialproof · cited by 11
- Nat.card_permproof · cited by 10
- IsGaloisGroup.card_eq_finrankproof · cited by 10
- Fintype.card_unitsproof · cited by 9
- pow_card_eq_oneproof · cited by 9
- Set.ncard_eq_toFinset_card'proof · cited by 9
- Finite.card_le_one_iff_subsingletonproof · cited by 6
- addOrderOf_dvd_natCardproof · cited by 6
- Nat.card_funproof · cited by 5