proposition: Lemma exprBn_comm x y n (cxy : comm x y) : (x - y) ^+ n = \sum_(i < n.+1) ((-1) ^+ i * x ^+ (n - i) * y ^+ i) *+ 'C(n, i).
proof: Proof. rewrite exprDn_comm; last exact: commrN. by apply: eq_bigr => i _; congr (_ *+ _); rewrite -commr_sign -mulrA -exprNn. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)