proposition: Lemma comm_subG A B G : A \subset G -> B \subset G -> [~: A, B] \subset G.
proof: Proof. by move=> sAG sBG; apply: subset_trans (der1_subG G); apply: commgSS. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)