proposition: Lemma lcoset_id x : x \in G -> x *: G = G.
proof: Proof. by move=> Gx; rewrite (lcoset_eqP (_ : x \in 1 *: G)) mul1g. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)