Theorems · Theorem · combinatorics
Nat.choose_symm
∀ {n k : ℕ}, k ≤ n → n.choose (n - k) = n.choose k- Defined in
- Mathlib.Data.Nat.Choose.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.factorialproof · cited by 616
- Nat.choosestatement and proof · cited by 494
- Nat.choose_eq_factorial_div_factorialproof · cited by 8
Cited by15
Results whose statement or proof uses this declaration.
- Nat.choose_le_middleproof · cited by 7
- Nat.choose_symm_of_eq_addproof · cited by 7
- Polynomial.bernoulli_defproof · cited by 4
- Polynomial.norm_coeff_le_choose_mul_mahlerMeasureproof · cited by 3
- Finset.sum_antidiagonal_choose_succ_nsmulproof · cited by 3
- bernoulli'_specproof · cited by 1
- Polynomial.sum_range_pow_eq_bernoulli_subproof · cited by 1
- bernsteinPolynomial.flipproof · cited by 1
- Polynomial.coeff_le_of_roots_leproof · cited by 1
- Nat.sum_range_choose_halfwayproof · cited by 1
- Multiset.multinomial_addproof · cited by 1
- AhlswedeZhang.infSum_compls_add_supSumproof · cited by 1