The theorem states that: If ''<math>f''(''n'')</math> is a time-constructible function, then there exists a [[decision problem]] which cannot be solved in worst-case deterministic time ''<math>f''(''n'')</math> but can be solved in worst-case deterministic time ''<math>f''(''n'')<sup>^2</supmath>. In other words, the complexity class [[DTIME]](''<math>f''(''n''))</math> is a strict subset of DTIME(''<math>f''(''n'')<sup>^2</supmath>). Note that ''<math>f''(''n'')</math> is at least ''n'', since smaller functions are never time-constructible.
Even more generally, it can be shown that if ''<math>f''(''n'')</math> is time-constructible, then <math>\operatorname{DTIME}\left(o\left(''\frac{f''(''n'')/}{\log ''f''(''n'')}\right)\right)</math> is properly contained in <math>\operatorname{DTIME}(''f''(''n''))</math>. For example, there are problems solvable in time ''n''<sup>2</sup> but not time ''n'', since ''n'' is in <math>o\left(''\frac{n''<sup>^2</sup>/}{\log ''{n''<sup>^2}}\right)</supmath>).
