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