
theorem
not X^3-1 splits_in F_Real
proof
now assume X^3-1 splits_in F_Real; then
  A: {1, zeta, zeta^2} c= the carrier of F_Real
                                  by lemroots3,LLsplit,FIELD_8:27;
  zeta in {1, zeta, zeta^2} by ENUMSET1:def 1;
  hence contradiction by A,FIELD_7:def 5;
  end;
hence thesis;
end;
