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