proposition: Lemma coset_default x : (x \in 'N(H)) = false -> coset H x = 1.
proof: Proof. move=> Nx; apply: val_inj. by rewrite val_insubd /= mem_rcosets /= genGid mulSGid ?normG ?Nx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)