proposition: Lemma monic_F2 p : p != 0 -> p \is monic.
proof: Proof. move=> p0; apply/negPn/negP => H. have {H} : lead_coef p == 0 by move/monicP/eqP : H; rewrite -F2_eq0. rewrite lead_coef_eq0; by apply/negP. Qed.
imports: mathcomp(all_ssreflect fingroup perm ssralg zmodp) mathcomp(matrix mxalgebra poly polydiv mxpoly)