proposition: Lemma quotientK A : A \subset 'N(H) -> coset H @*^-1 (A / H) = H * A.
proof: Proof. by rewrite -{8}ker_coset; apply: morphimK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)