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

theorem Th60:
  for X,Y1,Y2 be set holds
      comp(X,x,y,Y1\/Y2) = comp(X,x,y,Y1)\/comp(X,x,y,Y2)
proof
  let X,Y1,Y2 be set;
  thus comp(X,x,y,Y1\/Y2) c= comp(X,x,y,Y1)\/comp(X,x,y,Y2)
  proof
    let o;
    assume o in comp(X,x,y,Y1\/Y2);
    then consider x1,y1 be Surreal such that
    A1: o = (x1*y) +' (x*y1) +' -' (x1*y1) & x1 in X & y1 in Y1\/Y2 by Def14;
    y1 in Y1 or y1 in Y2 by A1,XBOOLE_0:def 3;
    then o in comp(X,x,y,Y1) or o in comp(X,x,y,Y2) by A1,Def14;
    hence thesis by XBOOLE_0:def 3;
  end;
  comp(X,x,y,Y1) c= comp(X,x,y,Y1\/Y2) &
  comp(X,x,y,Y2) c= comp(X,x,y,Y1\/Y2) by XBOOLE_1:7,Th59;
  hence thesis by XBOOLE_1:8;
end;
