End InternalProd.
Arguments complP {gT H A B}.
Arguments splitsP {gT B A}.
Arguments sdprod_normal_complP {gT G K H}.
Arguments dprodYP {gT K H}.
Arguments bigdprodYP {gT I P F}.
Section MorphimInternalProd.
Variables (gT rT : finGroupType) (D : {group gT}) (f : {morphism D >-> rT}).
Section OneProd.
Variables G H K : {group gT}.
Hypothesis sGD : G \subset D.

(* Specifications: *)
Lemma morphim_pprod : pprod K H = G -> pprod (f @* K) (f @* H) = f @* G.
Lemma morphim_coprime_sdprod :
K ><| H = G -> coprime #|K| #|H| -> f @* K ><| f @* H = f @* G.
Lemma injm_sdprod : 'injm f -> K ><| H = G -> f @* K ><| f @* H = f @* G.
Lemma morphim_cprod : K \* H = G -> f @* K \* f @* H = f @* G.
Lemma injm_dprod : 'injm f -> K \x H = G -> f @* K \x f @* H = f @* G.
Lemma morphim_coprime_dprod :
K \x H = G -> coprime #|K| #|H| -> f @* K \x f @* H = f @* G.