
theorem grad6:
deg(FAdj(F_Rat,{3-CRoot(2),zeta}), F_Rat) = 6
proof
set F = FAdj(F_Rat,{3-CRoot(2), zeta}), K = FAdj(F_Rat,{3-CRoot(2)});
A: deg(FAdj(F_Rat,{3-Root(2)}),F_Rat) = 3 by LL,minpolzeta,FIELD_6:67;
B: K = FAdj(F_Rat,{3-Root(2)}) by mmk;
FAdj(F_Rat,{3-CRoot(2), zeta})
    = FAdj(F_Rat,{3-CRoot(2)}\/{zeta}) by ENUMSET1:1
   .= FAdj(K,{zeta}) by FIELD_7:35; then
deg(F,F_Rat) = deg(F,K) * deg(K,F_Rat) by FIELD_7:30
            .= 6 by A,B,mml;
hence thesis;
end;
