Theorems · Theorem · combinatorics
Nat.choose_mul_factorial_mul_factorial
∀ {n k : ℕ}, k ≤ n → n.choose k * k.factorial * (n - k).factorial = n.factorial- Defined in
- Mathlib.Data.Nat.Choose.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.factorialstatement · cited by 616
- Nat.choosestatement · cited by 494
Cited by13
Results whose statement or proof uses this declaration.
- Complex.exp_addproof · cited by 55
- Nat.descFactorial_eq_factorial_mul_chooseproof · cited by 12
- Nat.choose_eq_factorial_div_factorialproof · cited by 8
- Nat.cast_chooseproof · cited by 6
- Nat.factorial_mul_factorial_dvd_factorialproof · cited by 6
- Nat.add_choose_mul_factorial_mul_factorialproof · cited by 5
- Nat.ascFactorial_eq_factorial_mul_chooseproof · cited by 3
- Nat.Prime.emultiplicity_choose'proof · cited by 2
- Nat.factorization_choose'proof · cited by 1
- Equiv.Perm.card_of_cycleType_singletonproof · cited by 1
- Ring.add_choose_eqproof · cited by 1
- Ring.choose_smul_chooseproof · cited by 1