H: MinPoly (3-Root(2),F_Rat) = X^3-2 by LL2, FIELD_6:52;

now :: thesis: 3-Root(2) is not Element of (FAdj (F_Rat,{2-Root(2)}))

assume 3-Root(2) is Element of (FAdj (F_Rat,{2-Root(2)})) ; :: thesis: contradiction
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; :: thesis: verum

end;

hence 3-Root(2) is not Element of (FAdj (F_Rat,{2-Root(2)})) ; :: thesis: verum