Section IntermediateField.
Variable M : {subfield L}.
Hypothesis (sKME : (K <= M <= E)%VS) (nKM : normalField K M).
Definition normalField_cast (x : gal_of E) : gal_of M := gal M x.
Canonical normalField_cast_morphism := Morphism normalField_castM.

Lemma normalField_ker : 'ker normalField_cast = 'Gal(E / M).