Prove that logical equivalence is a consisten congruence.
Refactor into more files to speed up dev cycle.
For no particularly good reason, stop depending on HT.
Add a new file for theory about the relationships between our different equivs.
The next step is generalized it. Generalize the notion of of pairs of closing substitutions that respect a relation on closed terms.
Make observational eq a record.
Prove logical eq contains observ eq, modulo some deeply annoying looking lemma.