proposition: Lemma util_C (n i j : nat) : (i <= j) -> (j <= n) -> ('C(n-i, j-i) * 'C(n, i) = 'C(n, j) * 'C(j, i)).
proof: Proof. move => ij jn. move: (binom_exchange i (j - i) (n - j)). by rewrite (subnKC ij)(subnKC jn) (addnC (j-i)) (addnBA _ ij) (subnK jn). Qed.
imports: mathcomp(all_ssreflect) mathcomp(ssralg poly ssrnum ssrint rat polyrcf) mathcomp(polyorder polydiv)