proposition: Lemma coset_norm xbar : xbar \subset 'N(H).
proof: Proof. case: xbar => /= _ /rcosetsP[x Nx ->]. by rewrite genGid mul_subG ?sub1set ?normG. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)