
theorem lemNor1e:
for F being Field
for p being linear Element of the carrier of Polynom-Ring F
holds F is SplittingField of p
proof
let F be Field, p be linear Element of the carrier of Polynom-Ring F;
reconsider K = F as FieldExtension of F by FIELD_4:6;
A: deg p = 1 by FIELD_5:def 1;
now let E be FieldExtension of F;
  assume p splits_in E & E is Subfield of F; then
  E is Subfield of F & F is Subfield of E by FIELD_4:7;
  hence E == F by FIELD_7:def 2;
  end;
then K is SplittingField of p by A,FIELD_8:def 1,FIELD_4:29;
hence thesis;
end;
