  When formalizing proofs with interactive theorem provers, it often happens
that extra background knowledge (declarative or procedural) about mathematical
concepts is employed without the formalizer explicitly invoking it, to help the
formalizer focus on the relevant details of the proof. In the contexts of
producing and studying a formalized mathematical argument, such mechanisms are
clearly valuable. But we may not always wish to suppress background knowledge.
For certain purposes, it is important to know, as far as possible, precisely
what background knowledge was implicitly employed in a formal proof. In this
note we describe an experiment conducted on the MIZAR Mathematical Library of
formal mathematical proofs to elicit one such class of implicitly employed
background knowledge: properties of functions and relations (e.g.,
commutativity, asymmetry, etc.).
