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

theorem Th34:
  x == y implies born_eq_set x = born_eq_set y
proof
  assume x==y;
  then born_eq_set x c= born_eq_set y c= born_eq_set x by Lm1;
  hence thesis by XBOOLE_0:def 10;
end;
