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If you're interested in a %covers that "does the right thing" (input, output, freeness, and checking of other type families in subgoals), I have a simple implementation of the %partial declaration. This declaration does the same thing as %total but does not perform the totality check. From it you get a "partial correctness" property: a %partial relation will either search forever or it will succeed.  — Tom 7 22:41, 17 October 2007 (EDT)