proposition: Lemma quotient_cent1 x : 'C[x] / H \subset 'C[coset H x].
proof: Proof. case Nx: (x \in 'N(H)); first exact: morphim_cent1. by rewrite coset_default // cent11T subsetT. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)