proposition: Lemma setI_subnormal G H K : K \subset G -> H <|<| G -> H :&: K <|<| K.
proof: Proof. move=> sKG /subnormalP[s Hs defG]; apply/subnormalP. exists (map (setIgr K) s); first exact: path_setIgr. rewrite (last_map (setIgr K)) defG. by apply: val_inj; rewrite /= (setIidPr sKG). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(fintype bigop finset fingroup morphism) mathcomp(automorphism quotient action commutator center)