End TraceAndNormMorphism.
Section TraceAndNormField.
Variables K E : {subfield L}.

(* Specifications: *)
Lemma galTrace_fixedField a :
a \in E -> galTrace K E a \in fixedField 'Gal(E / K).
Lemma galTrace_gal a x :
a \in E -> x \in 'Gal(E / K) -> galTrace K E (x a) = galTrace K E a.
Lemma galNorm_fixedField a :
a \in E -> galNorm K E a \in fixedField 'Gal(E / K).
Lemma galNorm_gal a x :
a \in E -> x \in 'Gal(E / K) -> galNorm K E (x a) = galNorm K E a.