End TraceAndNormField.
Definition normalField U V := [forall x in kAEndf U, x @: V == V]%VS.

Lemma kHom_to_gal K M E f :
(K <= M <= E)%VS -> normalField K E -> kHom K M f ->
{x | x \in 'Gal(E / K) & {in M, f =1 x}}.