Theorems · Theorem · combinatorics
Nat.add_choose_eq
∀ (m n k : ℕ), (m + n).choose k = ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal k, m.choose ij.1 * n.choose ij.2
Vandermonde's identity
- Defined in
- Mathlib.Data.Nat.Choose.Vandermonde
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Polynomialproof · cited by 5,681
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Polynomial.Xproof · cited by 1,639
- Polynomial.coeffproof · cited by 1,045
- Nat.choosestatement and proof · cited by 494
- pow_addproof · cited by 315
- Finset.HasAntidiagonal.antidiagonalstatement and proof · cited by 218
- Polynomial.coeff_mulproof · cited by 29
- Nat.cast_idproof · cited by 12
- Polynomial.coeff_X_add_one_powproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Nat.sum_range_choose_sqproof · cited by 0
- Polynomial.hasseDeriv_mulproof · cited by 0