Any two terms in a STLC with unit, products and functions (and no base types) are equal.
I didn't find a quick reference for this, so I wrote a proof here: github.com/nachivpn/coher
Comments welcome!
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I just want to say this Agda looks really nice! I like the fact that you lean a bit on words - I find Agda code that leans in the other direction quite impenetrable!

