
theorem
not F_Complex is SplittingField of X^3-2
proof
set F = FAdj(F_Rat,{3-CRoot(2), zeta});
now assume A: F_Complex is SplittingField of X^3-2;
  X^3-2 splits_in F by 32split,FIELD_8:def 1; then
  F_Complex == F by A,FIELD_8:def 1; then
  F_Complex is Subfield of F by FIELD_7:def 2; then
  the carrier of F_Complex c= the carrier of F by EC_PF_1:def 1;
  hence contradiction by ff;
  end;
hence thesis;
end;
