proposition: Lemma im_coset : coset @* 'N(A) = setT.
proof: Proof. by apply/setP=> xbar; case: (cosetP xbar) => x Nx ->; rewrite inE mem_morphim. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)