proposition: Lemma lcoset_transl x y z : x \in y *: G -> (x \in z *: G) = (y \in z *: G).
proof: Proof. by move=> Gyx; rewrite -2!(lcoset_sym z) (lcoset_eqP Gyx). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)