You take a set S and partition it into two subsets, A and B, so that each element uniquely belongs to either of them. For each element of S it is true that "not-not-in-A -> in-A". Can this be shown to be true in MLTT? I don't know much about setoids to show it, but if it can't, that's the problem of MLTT, not mine. In the context of this proof, it is true.