
theorem
for F being Field,
    E being F-finite FieldExtension of F
holds E is F-normal iff
      for K being FieldExtension of E
      for h being F-fixing Monomorphism of E,K holds h is Automorphism of E
proof
let F be Field, E be F-finite FieldExtension of F;
now assume E is F-normal; then
   ex p being non constant Element of the carrier of Polynom-Ring F
      st E is SplittingField of p by lemNor1;
   hence for K being FieldExtension of E
      for h being F-fixing Monomorphism of E,K holds h is Automorphism of E
    by lemNor2;
   end;
hence thesis by lemNor3;
end;
