
theorem lemNor2bb:
for F being Field,
    E being FieldExtension of F,
    K being F-extending FieldExtension of E
for p being non constant Element of the carrier of Polynom-Ring F
st p splits_in E holds Roots(K,p) = Roots(E,p)
proof
let F be Field, E be FieldExtension of F,
    K be F-extending FieldExtension of E;
let p be non constant Element of the carrier of Polynom-Ring F;
assume AS: p splits_in E; then
p splits_in K by FIELD_8:19;
hence thesis by AS,FIELD_8:29;
end;
