Section Subnormal.
Variable gT : finGroupType.
Implicit Types (A B C D : {set gT}) (G H K : {group gT}).
Let setIgr H G := (G :&: H)%G.
Let sub_setIgr G H : G \subset H -> G = setIgr H G.

Lemma subnormalEr G H : H <|<| G ->
H :=: G \/ (exists K : {group gT}, [/\ H <|<| K, K <| G & K \proper G]).