Occurrence in Polish Notation has Unique Scope
Let $\mathbf A$ be a well-formed formula of $\FF$.
Let $a$ be an occurrence in $\mathbf A$.
Then $a$ has a unique scope.
- $a \mathbf A_1 \cdots \mathbf A_n$
for some well-formed formulas $\mathbf A_1, \ldots, \mathbf A_n$.
By Unique Readability for Polish Notation, the $\mathbf A_i$ are uniquely determined.
Then $\mathbf A' = a \mathbf A_1 \cdots \mathbf A_n$ is a well-formed part of $\mathbf A$.
Moreover, any well-formed part of $\mathbf A$ containing $a$ must contain $\mathbf A'$.
Hence $\mathbf A'$ is the scope of $a$.