
theorem mp:
MinPoly(2-Root(2),F_Rat) = X^2-2
proof
Ext_eval(X^2-2,2-Root(2))
  = (2-Root(2))|^(1+1) - 2 by LKX2ext
 .= (2-Root(2))|^1 * (2-Root(2))|^1 - 2 by BINOM:10
 .= (2-Root(2)) * (2-Root(2))|^1 - 2 by BINOM:8
 .= (2-Root(2)) * (2-Root(2)) - 2 by BINOM:8
 .= (sqrt 2)^2 - 2 by SQUARE_1:def 1
 .= 2 - 2 by SQUARE_1:def 2
 .= 0.F_Real;
hence thesis by FIELD_6:52;
end;
