Edit for context:
An expression in this context is any finite sequence of symbols of the language in question.
"A designator is an expression which is either a term or a formula. Every designator has the form $uv$1...$v$n where $u$ is a symbol and the $v$i are designators, and n is a natural number determined by $u$. For example, if $u$ is a variable, $n = 0$; if $u$ is a $k$-ary function symbol, $n = k$; if $u$ is the existential quantifier, $n = 2$. We call $n$ the index of $u$. We say two expressions are compatible if one can be obtained from the other by adding an expression to the right of the other (possibly the empty expression). If $uv$ and $u'v'$ are compatible, then $u$ and $u'$ are compatible. If $uv$ and $uv'$ are compatible, then $v$ and $v'$ are compatible."
The problem simply reads:
Show that if $uv$ and $vv'$ are designators, then either $v$ or $v'$ is the empty expression.
I don't see why this result is so, I'd like a hint, and if possible, a proof.