Theorems · Theorem · combinatorics
Nat.multinomial_insert
∀ {α : Type u_1} {s : Finset α} {a : α} [inst : DecidableEq α],
a ∉ s → ∀ (f : α → ℕ), Nat.multinomial (insert a s) f = (f a + ∑ i ∈ s, f i).choose (f a) * Nat.multinomial s f- Defined in
- Mathlib.Data.Nat.Choose.Multinomial
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Nat.choosestatement and proof · cited by 494
- Finset.cons_eq_insertproof · cited by 59
- Nat.multinomialstatement and proof · cited by 34
- Nat.multinomial_consproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Finsupp.multinomial_updateproof · cited by 2
- DividedPowerAlgebra.prod_dpproof · cited by 1
- Multiset.multinomial_nsmulproof · cited by 1
- DividedPowers.prod_dpowproof · cited by 0