I'd love to see some additional features:
- I'm currently at the excercise 9.1, and this far PUSH is always the only operation you can do when dragging from an outer scope to an inner one. Seems pretty fundamental. (To the extent that explicit mentions of "pushing" is not even normally mentioned in textual proofs?) Could this be streamlined somehow, for example applying PUSH automatically just with the drag & drop operation from outer to inner scope?
- Instead of a linear "achievement history", keep records of all produced proofs for each lemma. Highlight the one with the smallest amount of "rules".
- It seems to allow circular proofs by default. Surely this can be detected using a dependency graph?
- Speaking of dependency graphs, I'd love to explore reverse mathematics using this kind of an interactive tool. Maybe add some challenge by counting not only the amount of rules, but amount of axioms/basic rules of inference used, and counting also the size of the whole dependency graph of each proof. Maybe there could be separate record-keeping for different sets of axioms.