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> It is not difficult to keep the notation sane in formalizations based on set theory.

Keeping notation sane is, of course, very important. I think keeping notation sane is harder than it might first appear, but it is certainly possible.

One interesting trick used by Metamath's set.mm is to define variables that look similar to operators but can be defined for purposes of a particular proof (e.g., as hypotheses). For example, + underline, * underline, and so on.

For an example, see theorem grpridd, "Deduce right identity from left inverse and left identity in an associative structure (such as a group)." http://us.metamath.org/mpeuni/grpridd.html - the hypotheses include statements about "+ underscore", and lead to a proof about + underscore.






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