Section InternalProd.
Variable gT : finGroupType.
Implicit Types A B C : {set gT}.
Implicit Types G H K L M : {group gT}.
Local Notation pprod := (partial_product gT).
Local Notation sdprod := (semidirect_product gT) (only parsing).
Local Notation cprod := (central_product gT) (only parsing).
Local Notation dprod := (direct_product gT) (only parsing).
(* Properties of the remainders *)
(* Complements, and splitting. *)

Lemma complP H A B :
reflect (A :&: H = 1 /\ A * H = B) (H \in [complements to A in B]).