Right now System E is formulated as a bunch of axioms.
However, I believe it would more sensible for it to be formulated as a type class such as Group.
All of the theorems would more or less be the same, but proofs from LeanEuclid could more readily be used to prove theorems about the EuclideanSpace typeclass.
Additionally, it would make it easier to construct models of System E and prove the consistency of System E and/or that it has been properly formalized.
I understand that this may be beyond the scope of the project, but I would be willing to do this in a separate branch and make a pull request.