proposition: Lemma cosetpre_normal C D : (coset H @*^-1 C <| coset H @*^-1 D) = (C <| D).
proof: Proof. by rewrite morphpre_normal ?sub_im_coset. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)