reserve A,B,O for Ordinal,
        o for object,
        x,y,z for Surreal,
        n,m for Nat;
reserve d,d1,d2 for Dyadic;
reserve i,j for Integer,
        n,m,p for Nat;

theorem Th36:
  ex n st uDyadic.d in Day n
proof
  per cases;
  suppose d >=0;
    hence thesis by Lm6;
  end;
  suppose d < 0;
    then consider n such that
A1: uDyadic.-d in Day n by Lm6;
    take n;
    uDyadic.-d = - uDyadic.d by Th27;
    then - - uDyadic.d in Day n by A1,SURREALR:11;
    hence thesis;
  end;
end;
