proposition: Lemma quotient_cent1s A x : A \subset 'C[x] -> A / H \subset 'C[coset H x].
proof: Proof. by move=> sAC; apply: subset_trans (quotientS sAC) (quotient_cent1 x). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)