Vandermonde's identity #
In this file we prove Vandermonde's identity (Nat.add_choose_eq):
(m + n).choose k = ∑ (i, j) ∈ antidiagonal k, m.choose i * n.choose j
We follow the algebraic proof from https://en.wikipedia.org/wiki/Vandermonde%27s_identity#Algebraic_proof .
theorem
Nat.add_choose_eq
(m : ℕ)
(n : ℕ)
(k : ℕ)
:
(m + n).choose k = ∑ ij ∈ Finset.antidiagonal k, m.choose ij.1 * n.choose ij.2
Vandermonde's identity