Variables E K : {subfield L}.
Hypothesis galKE : galois K E.
Section IntermediateField.
Variable M : {subfield L}.
Hypothesis (sKME : (K <= M <= E)%VS) (nKM : normalField K M).

Lemma normalField_galois : galois K M.
Definition normalField_cast (x : gal_of E) : gal_of M := gal M x.