I would use a comma on that one, since the "solid proof" part doesn't stand on it's own.
In other words, if you can't use a period (full stop) then you can't use a semi-colon.
There is one exception that I can think of (and I think you mentioned it): In lists where any element has a comma, you can use a semi-colon to offset the elements.
I bought the A, B, and C; the D; and the E.
As far as colons go, what's on the left must be gramatically complete. What's on the right is a definition of what's on the left.
See this site for a few examples (and examples of colons too):
http://www.grammartips.homestead.com/colons.html