proposition: Lemma gcore_normal A G : A \subset G -> gcore A G <| G.
proof: Proof. by move=> sAG; rewrite /normal gcore_norm (subset_trans (gcore_sub A G)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)