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

theorem Th70:
  0_No < x & y < z implies y*x < z*x
proof
  assume 0_No < x & y < z;
  then 0_No*z+x*y < 0_No*y+x*z by Th51;
  hence thesis;
end;
