Section NormalComplement.
Variables K H G : {group gT}.
Hypothesis complH_K : H \in [complements to K in G].
End NormalComplement.
(* Semi-direct product *)
(* Central product *)
Canonical cprod_law := Monoid.Law cprodA cprod1g cprodg1.
Canonical cprod_abelaw := Monoid.ComLaw cprodC.
(* Direct product *)

Lemma dprod_normal2 A B G : A \x B = G -> A <| G /\ B <| G.