We provide a reformulation and a formalization of the classical result by Juhani Karhum\"aki characterizing intersections of two languages of the form $\{x,y\}^*\cap \{u,v\}^*$. We use the terminology of morphisms which allows to formulate the result in a shorter and more transparent way, and we formalize the result in the proof assistant Isabelle/HOL.

中文翻译：

---

二元交集形式化

我们提供了 Juhani Karhum\"aki 的经典结果的重新表述和形式化，表征了 $\{x,y\}^*\cap \{u,v\}^*$ 形式的两种语言的交集。我们使用态射的术语允许以更短、更透明的方式表述结果，我们在证明助手 Isabelle/HOL 中将结果形式化。