> but a fully-expressed typed proof outline is enough to quickly verify correctness of the proof. Yes, implementing that is the difficult part. I'm not saying

> but a fully-expressed typed proof outline is enough to quickly verify correctness of the proof. Yes, implementing that is the difficult part. I'm not saying it's infeasible - I'm saying it's very difficult. Writing provably correct software is also very difficult. This kind of theorem checking is becoming more common for theorems in e.g. combinatorics, but it's still very uncommon due to the added effort.