Definition:Well-Formed Part

Definition
Let $\mathcal L$ be a formal language with alphabet $\mathcal A$.

Let $\mathbf A$ be a well-formed word of $\mathcal L$.

Let $\mathbf B$ be a substring of $\mathbf A$.

Then $\mathbf B$ is a well-formed part of $\mathbf A$ iff $\mathbf B$ is a well-formed word of $\mathcal L$.

In the contexts of propositional calculus and predicate calculus, where the term used is well-formed formula, the term subformula can often be seen.