As a result, if the function d is taken to represent distance, we obtain the expected results about congruence and betweenness. Thus, although we cannot talk about numbers in Hilbert's geometry (there are no such entities to quantify over), there is a metatheoretic result that associates assertions about distances with what can be said in the theory. Field calls such numerical claims abstract counterparts of purely geometric assertions, and they can be used to draw conclusions about purely geometrical claims in a smoother way. Indeed, because of the representation theorem, conclusions about space, statable without real numbers, can be drawn far more easily than we could achieve by a deflationary proof from Hilbert's axioms. This illustrates Field's point that the usefulness of mathematics derives from shortening derivations (Field 1980, pp. 24–29).