`` So let us suppose that is unsatisfiable. By Lemma I, there is a canonical derivation from . Since is unsatisfiable and is a subset of all the sentences appearing in , there is no model of the set of all such sentences. By Lemma II, then, there is no model of the set of quantifier-free sentences in that matches . If we could prove a proposition to the effect that
then we should have proved the completeness theorem, for we should know that some finite set of the quantifier-free sentences in is unsatisfiable" (p. 135).
Let's make sure we get this