proposition: Lemma normalI G A B : A <| G -> B <| G -> A :&: B <| G.
proof: Proof. by case/andP=> sAG nAG /andP[_ nBG]; rewrite /normal subIset ?sAG // normsI. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)