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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.

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  • $\begingroup$ Without access to the book, it is unclear what you are asking. Please provide more context for the question, and any attempts you have made. $\endgroup$ – Graham Kemp Oct 16 '19 at 23:05
  • $\begingroup$ @graham-kemp I have edited the post with the definition given in the book. Apologies, I assumed it was common knowledge. $\endgroup$ – Caroline.T Oct 17 '19 at 10:56
  • $\begingroup$ Sadly, a lot of logic has different names for the same object or the same names for the same object. What do you mean by an 'expression' here? $\endgroup$ – Shiranai Oct 17 '19 at 18:05
  • $\begingroup$ See similar post. $\endgroup$ – Mauro ALLEGRANZA Oct 18 '19 at 8:07
  • $\begingroup$ @shiranai An expression here is any finite sequence of symbols of a given language. I wasn't aware so much of this depended on the text in question. Thank you, and apologies $\endgroup$ – Caroline.T Oct 18 '19 at 12:20

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