Theorems · Theorem · combinatorics
Nat.binomial_eq
∀ {α : Type u_1} {f : α → ℕ} {a b : α} [inst : DecidableEq α],
a ≠ b → Nat.multinomial {a, b} f = (f a + f b).factorial / ((f a).factorial * (f b).factorial)- Defined in
- Mathlib.Data.Nat.Choose.Multinomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- CommMonoidproof · cited by 2,264
- Nat.factorialstatement and proof · cited by 616
- Nat.multinomialstatement · cited by 34
- Finset.sum_pairproof · cited by 11
- Finset.prod_pairproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Nat.binomial_eq_chooseproof · cited by 3