Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck.

大型形式化数学库由数百万个原子推理步骤组成，这些原子推理步骤产生相应数量的经证明的陈述（引理）。类似于非正式数学实践，此类陈述中只有一小部分被正式数学家命名并在以后的证明中重复使用。在这项工作中，我们建议并实施了一些标准，这些标准定义了HOL Light引理在证明进一步定理方面的估计有用性。我们使用这些标准来挖掘HOL Light和Flyspeck中引理的大推论图库，最多可将成千上万的最佳引理添加到语句池中，这些语句可在以后的证明中重复使用。我们表明，结合基于学习的相关性过滤，此类方法显着增强了大型正式数学库（例如Flyspeck）上新猜想的自动定理证明。