proposition: Lemma coset_kerr x y : y \in H -> coset H (x * y) = coset H x.
proof: Proof. move=> Hy; case Nx: (x \in 'N(H)); first by rewrite mkerr ?ker_coset. by rewrite !coset_default ?groupMr // (subsetP (normG H)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)