proposition: Lemma coset_idr x : x \in 'N(H) -> coset H x = 1 -> x \in H.
proof: Proof. by move=> Nx Hx1; rewrite -ker_coset mem_morphpre //= Hx1 set11. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)