Section TraceAndNormField.
Variables K E : {subfield L}.
End TraceAndNormField.
Definition normalField U V := [forall x in kAEndf U, x @: V == V]%VS.

Lemma splitting_normalField E K :
(K <= E)%VS ->
reflect (exists2 p, p \is a polyOver K & splittingFieldFor K p E)
(normalField K E).