proposition: Lemma cosetpre_cents A C : coset H @*^-1 C \subset 'C(A) -> C \subset 'C(A / H).
proof: Proof. by apply: morphpre_cents; rewrite ?sub_im_coset. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)