proposition: Lemma mem_quotient x G : x \in G -> coset H x \in G / H.
proof: Proof. by move=> Gx; rewrite -imset_coset imset_f. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)