reserve A,B,C for Ordinal,
        o for object,
        x,y,z,t,r,l for Surreal,
        X,Y for set;

theorem
  for x1,x2,y1,y2 be Surreal st
    x1==x2 & y1==y2 holds x1+y1 == x2+y2 by Th43;
