reserve A,B for Ordinal,
        o for object,
        x,y,z for Surreal,
        n for Nat,
        r,r1,r2 for Real;

theorem Th1:
  uReal.r in Day omega
proof
  born_eq sReal.r c= born sReal.r c= omega by SURREALO:def 5,SURREALN:49;
  then
A1:born_eq sReal.r c= omega by XBOOLE_1:1;
  uReal.r = Unique_No sReal.r by SURREALN:def 7;
  then born_eq sReal.r = born_eq uReal.r = born uReal.r
    by SURREALO:def 10,33,48;
  then uReal.r in Day born uReal.r c= Day omega by A1,SURREAL0:def 18,35;
  hence thesis;
end;
