proposition: Lemma lead_coef_F2 p q : size p = size q -> lead_coef p = lead_coef q.
proof: Proof. move=> X. case/boolP : (size p == O) => Y. - move: X; rewrite (eqP Y) => /esym/eqP; rewrite size_poly_eq0 => /eqP ->. by move: Y; rewrite size_poly_eq0 => /eqP ->. - rewrite !size_lead_coef_F2 //; last by apply/eqP. rewrite -X; by apply/eqP. Qed.
imports: mathcomp(all_ssreflect fingroup perm ssralg zmodp) mathcomp(matrix mxalgebra poly polydiv mxpoly)