I feel that calling the final step a "sanity check" underrates its significance. To me, it implies that you essentially have the proof, and you are just looking

I feel that calling the final step a "sanity check" underrates its significance. To me, it implies that you essentially have the proof, and you are just looking for confirmation that it is sound and whether there are some edge cases to finish off. In contrast, I would say that it is the first point at which you understand how the half-remembered fragments of the proof can be put together to make an unassailable case for the proposition. Until then, it is as if you are groping around in the dark, trying to remember what the room looked like when the light was on (I know what it's like, as I have frequently been in that situation!) These answers are the sort one might expect from something that has a vast memory for what it has seen before, and an ability to draw huge networks of syntax-level associations and generalizations from all that text, but is not so strong on semantic associations and generalizations that are not manifest at the level of syntax. What surprises me is how successful that has been.