proposition: Lemma groupJ x y : x \in G -> y \in G -> x ^ y \in G.
proof: Proof. by move=> Gx Gy; rewrite !in_group. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)