Theorems · Theorem · combinatorics
Nat.choose_eq_factorial_div_factorial
∀ {n k : ℕ}, k ≤ n → n.choose k = n.factorial / (k.factorial * (n - k).factorial)- Defined in
- Mathlib.Data.Nat.Choose.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.factorialstatement and proof · cited by 616
- Nat.choosestatement and proof · cited by 494
- Nat.factorial_posproof · cited by 99
- Nat.choose_mul_factorial_mul_factorialproof · cited by 13
Cited by8
Results whose statement or proof uses this declaration.
- Nat.choose_symmproof · cited by 15
- Nat.binomial_eq_chooseproof · cited by 3
- Nat.add_chooseproof · cited by 3
- IsNilpotent.exp_add_of_commuteproof · cited by 3
- PowerSeries.exp_mul_exp_eq_exp_addproof · cited by 2
- Nat.factorization_choose_eq_zero_of_ltproof · cited by 2
- sum_range_powproof · cited by 2
- sub_one_mul_padicValNat_choose_eq_sub_sum_digits'proof · cited by 1