proposition: Lemma commgS A B C : B \subset C -> [~: A, B] \subset [~: A, C].
proof: Proof. by move=> sBC; rewrite genS ?imset2S. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)