
theorem nnn:
not 3-Root(2) is Element of FAdj(F_Rat,{2-Root(2)})
proof
H: MinPoly(3-Root(2),F_Rat) = X^3-2 by LL2,FIELD_6:52;
now assume 3-Root(2) is Element of FAdj(F_Rat,{2-Root(2)}); then
  reconsider a = 3-Root(2) as Element of FAdj(F_Rat,{2-Root(2)});
  I: deg MinPoly(a,F_Rat) = 3 by H,LL,mmv;
  deg(FAdj(F_Rat,{2-Root(2)}),F_Rat) = 2 by LL,mp,FIELD_6:67;
  hence contradiction by I,mmu,INT_2:27;
  end;
hence thesis;
end;
