Theorems · Theorem · combinatorics
Nat.multinomial_cons
∀ {α : Type u_1} {s : Finset α} {a : α} (ha : a ∉ s) (f : α → ℕ),
Nat.multinomial (Finset.cons a s ha) f = (f a + ∑ i ∈ s, f i).choose (f a) * Nat.multinomial s f- Defined in
- Mathlib.Data.Nat.Choose.Multinomial
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Finset.sumstatement and proof · cited by 5,195
- Finset.prodproof · cited by 2,356
- mul_assocproof · cited by 1,667
- Nat.factorialproof · cited by 616
- Nat.choosestatement and proof · cited by 494
- Finset.consstatement and proof · cited by 221
- mul_left_commproof · cited by 184
- Nat.factorial_posproof · cited by 99
- Finset.sum_consproof · cited by 84
- Finset.prod_consproof · cited by 60
- Nat.multinomialstatement and proof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- Nat.multinomial_insertproof · cited by 4
- Nat.multinomial_singletonproof · cited by 2
- Finset.sum_pow_eq_sum_piAntidiag_of_commuteproof · cited by 1