Theorems · Theorem · logic and foundations
Nat.card_fun
∀ {α : Type u_1} {β : Type u_2} [Finite α], Nat.card (α → β) = Nat.card β ^ Nat.card α- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- Fintype.ofFiniteproof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
- Finset.prod_constproof · cited by 154
- Finset.card_univproof · cited by 58
- Nat.card_piproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- Module.natCard_eq_pow_finrankproof · cited by 3
- AddSubgroup.index_range_nsmulproof · cited by 1
- RegularWreathProduct.cardproof · cited by 1
- Projectivization.card_of_finrankproof · cited by 1
- Subgroup.index_center_le_powproof · cited by 1