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

theorem
  x < 0_No & y < z implies z*x < y*x
proof
  assume x <0_No & y < z;
  then  x*z+0_No*y < x*y+0_No*z by Th51;
  hence thesis;
end;
