( I think this got marked as spam yesterday because I used HTML formatting,
so I'm trying again.
There was a longer transcript of a j session using the logic stuff. I'll
repost that on the programming list. )

Here's a derivation of the quadratic formula in J.

https://github.com/tangentstorm/tangentlabs/blob/master/j/quadratic.ijs#L132

I also use this quite a bit on IRC:

https://github.com/tangentstorm/tangentlabs/blob/master/j/logic.ijs

The majority of the lines in those files are just assertions, using a
slightly modified version of the 'assert' verb in the z locale.
A large portion of the lines are in fact identities.
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