As someone who's used proof checkers a fair amount, if you don't have some high level idea about the proof, it's an open problem, and the hard part isn't some extremely tedious finite case analysis, it's extremely unlikely you'll get anywhere by trying to mechanize by throwing stuff against the wall to get it to typecheck. When people talk about mathematics being a closed formal system as though this trivializes any creative component, what they're omitting is that in type theory like that used by Lean or Rocq, there are two kinds of terms (match statements proving dependent elimination and fixpoints that provide proof by induction) where there's no real way to infer the type from the term. i.e., there are cases where you have to get creative and try to prove something more general than what you actually care about in order to get the proof about the original case to go through. What does "more general" mean? It could mean anything... that's the problem. That's why it's usually advantageous to reformulate the problem in terms of a different abstraction and build on top of existing results, knowing a lot about the literature and the way these kinds of problems tend to be attacked, rather than just chuck random terms over to a proof assistant and hope for the best.