
theorem
not X^3-2 splits_in FAdj(F_Rat,{3-Root(2)})
proof
set F = FAdj(F_Rat,{3-Root(2)});
B: the carrier of F c= the carrier of F_Real by EC_PF_1:def 1;
now assume X^3-2 splits_in F; then
  Roots(F,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,X^3-2) by ENUMSET1:def 1;
  hence contradiction by B,lemnotsplit;
  end;
hence thesis;
end;
