
theorem
not X^3-2 splits_in F_Real
proof
now assume X^3-2 splits_in F_Real; then
  Roots(F_Real,X^3-2) = {3-Root(2), 3-Root(2) * zeta, 3-Root(2) * zeta^2}
     by LLsplit,FIELD_8:29,lemroots; then
  3-Root(2) * zeta in Roots(F_Real,X^3-2) by ENUMSET1:def 1;
  hence contradiction by lemnotsplit;
  end;
hence thesis;
end;
