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 *)
Canonical dprod_law := Monoid.Law dprodA dprod1g dprodg1.
Canonical dprod_abelaw := Monoid.ComLaw dprodC.

Lemma bigdprodW I (r : seq I) P F G :
\big[dprod/1]_(i <- r | P i) F i = G -> \prod_(i <- r | P i) F i = G.