Theorems · Theorem · combinatorics
Nat.binomial_eq_choose
∀ {α : Type u_1} {f : α → ℕ} {a b : α} [inst : DecidableEq α],
a ≠ b → Nat.multinomial {a, b} f = (f a + f b).choose (f a)- Defined in
- Mathlib.Data.Nat.Choose.Multinomial
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 58 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
- Nat.factorialproof · cited by 616
- Nat.choosestatement · cited by 494
- add_tsub_cancel_leftproof · cited by 42
- Nat.multinomialstatement · cited by 34
- Nat.choose_eq_factorial_div_factorialproof · cited by 8
- Nat.binomial_eqproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.coeff_add_powproof · cited by 1
- Nat.binomial_succ_succproof · cited by 0
- Nat.succ_mul_binomialproof · cited by 0