 The formula_1-lemma states that every uncountable collection of finite sets contains an uncountable formula_1-system.The formula_1-lemma is a combinatorial set-theoretic tool used in proofs to impose an upper bound on the size of a collection of pairwise incompatible elements in a forcing poset.It may for example be used as one of the ingredients in a proof showing that it is consistent with Zermelo–Fraenkel set theory that the continuum hypothesis does not hold.