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 subnormalP H G :
reflect (exists2 s, normal.-series H s & last H s = G) (H <|<| G).