proposition: Lemma genD A B : A \subset <<A :\: B>> -> <<A :\: B>> = <<A>>.
proof: Proof. by move=> sAB; apply/eqP; rewrite eqEsubset genS (subsetDl, gen_subG). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)