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

theorem
  comp({z},x,y,{t}) = { z*y + x*t - z*t}
proof
  A1:comp({z},x,y,{t}) c= { z*y + x*t - z*t}
  proof
    let o;
    assume o in comp({z},x,y,{t});
    then consider  x1,y1 be Surreal such that
    A2: o = x1*y + x*y1 - x1*y1 & x1 in {z} & y1 in {t} by Def15;
    x1=z & y1=t by A2,TARSKI:def 1;
    hence thesis by A2,TARSKI:def 1;
  end;
  z in {z} & t in {t} by TARSKI:def 1;
  then z*y + x*t - z*t in comp({z},x,y,{t}) by Def15;
  hence thesis by A1, ZFMISC_1:33;
end;
