Definition:Well-Formed Part/Proper Well-Formed Part

Definition

Let $\FF$ be a formal language with alphabet $\AA$.

Let $\mathbf A$ be a well-formed formula of $\FF$.

Let $\mathbf B$ be a well-formed part of $\mathbf A$.

Then $\mathbf B$ is a proper well-formed part of $\mathbf A$ if and only if $\mathbf B$ is not equal to $\mathbf A$.

Also known as

In sources where WFFs are referred to as formulas, the term proper subformula can often be seen.

Sources

• 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.4$: Logical equivalence and substitution: Definition $2.4.5$
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.3.2$: Definition $2.30$