proposition: Lemma normal_cosetpre M : H <| coset H @*^-1 M.
proof: Proof. by rewrite -{1}ker_coset; apply: ker_normal_pre. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)