Theorems · Theorem · combinatorics
Set.powersetCard.card
∀ (α : Type u_1) (n : ℕ), Nat.card ↑(Set.powersetCard α n) = (Nat.card α).choose n
- Defined in
- Mathlib.Data.Set.PowersetCard
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Fintypeproof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Finset.cardproof · cited by 2,327
- Fintype.cardproof · cited by 1,386
- Nat.cardstatement and proof · cited by 844
- Nat.choosestatement and proof · cited by 494
- Infiniteproof · cited by 352
- Nat.card_eq_fintype_cardproof · cited by 200
- Set.powersetCardstatement and proof · cited by 100
- Fintype.card_uniqueproof · cited by 59
Cited by5
Results whose statement or proof uses this declaration.
- Set.powersetCard.nontrivialproof · cited by 2
- Set.powersetCard.isPretransitive_alternatingGroupproof · cited by 1
- exteriorPower.finrank_eqproof · cited by 1
- Set.powersetCard.nontrivial_iffproof · cited by 0
- Set.powersetCard.eq_empty_iffproof · cited by 0