
theorem grad4:
deg(FAdj(F_Rat,{2-CRoot(2),zeta}),F_Rat) = 4
proof
set F = FAdj(F_Rat,{2-CRoot(2), zeta}), K = FAdj(F_Rat,{2-CRoot(2)});
A: X^2-2 = MinPoly(2-CRoot(2),F_Rat) by mp,mmv;
   F = FAdj(F_Rat,{2-CRoot(2)}\/{zeta}) by ENUMSET1:1
    .= FAdj(K,{zeta}) by FIELD_7:35;
hence deg(F,F_Rat) = deg(F,K) * deg(K,F_Rat) by FIELD_7:30
                  .= 2 * 2 by A,LL,FIELD_6:67,mmmza
                  .= 4;
end;
