Theorems · Theorem · combinatorics
Sym.card_sym_eq_multichoose
∀ (α : Type u_2) (k : ℕ) [inst : Fintype α] [inst_1 : Fintype (Sym α k)], Fintype.card (Sym α k) = (Fintype.card α).multichoose k
For any fintype α of cardinality n, card (Sym α k) = multichoose (card α) k.
- Defined in
- Mathlib.Data.Sym.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement and proof · cited by 1,386
- Symstatement and proof · cited by 150
- Fintype.card_congrproof · cited by 67
- Fintype.equivFinproof · cited by 51
- Nat.multichoosestatement · cited by 14
- Sym.equivCongrproof · cited by 5
- Sym.card_sym_fin_eq_multichooseproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Sym.card_sym_eq_chooseproof · cited by 1
- Sym.natCard_sym_eq_multichooseproof · cited by 1
- Finset.card_finsuppAntidiag_nat_eq_multichooseproof · cited by 0