Clutch

CM, thanks for your comments; sorry for asking such a vague question. Here's what I was thinking: constructivist results often seem to consist in showing how some proof previously accepted on non-constructive grounds is in fact provable within constructive scruples as well. These discoveries can be interesting and surprising. I just took it that there's no general way of telling which NC proofs are constructively recoverable, and which are not. Is that right? Are there specific very handy proofs that are known or conceded to be unrecoverable, even by constructivists?

That's still pretty vague, but clearer than before, I hope.