I added the following to the preamble:
\newref{claim}{name=Claim~}
\newref{defn}{name=Definition~}
\newref{prop}{name=Proposition~}
\newref{thm}{name=Theorem~}
\newref{lem}{name=Lemma~}
and use formatted cross-references when I insert a reference.
It does exactly what I want for some of the items, but sometimes the references will show up with question marks where the number should be, such as "...according to Proposition ??..."
Does anyone know why this is happening or how I can fix it?