proposition: Lemma normalS G H K : K \subset H -> H \subset G -> K <| G -> K <| H.
proof: Proof. by move=> sKH sHG /andP[_ nKG]; rewrite /(K <| _) sKH (subset_trans sHG). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)