Section FieldAutomorphism.
Variables (u : {rmorphism algC -> algC}) (gT rT : finGroupType).
Variables (G K H : {group gT}) (f : {morphism G >-> rT}) (R : {group rT}).
Implicit Types (phi : 'CF(G)) (S : seq 'CF(G)).
Local Notation "phi ^u" := (cfAut u phi) (at level 3, format "phi ^u").
Hypothesis KxH : K \x H = G.

Lemma cfAutDprodl (phi : 'CF(K)) : (cfDprodl KxH phi)^u = cfDprodl KxH phi^u.