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