What is Fundamental lemma of sieve theory?

In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular problems. Halberstam & Richertwrite:

A curious feature of sieve literature is that while there is frequent use of Brun's method there are only a few attempts to formulate a general Brun theorem ; as a result there are surprisingly many papers which repeat in considerable detail the steps of Brun's argument.

Diamond & Halberstamattribute the terminology Fundamental Lemma to Jonas Kubilius.