>How do you make sure that the LLM doesn't reward hack a proof using these workarounds?
I'm not sure what you mean exactly? There is no soundness issue here, the fact that `sqrt -1` is defined to be 0 does not have any impact on what statements about `sqrt x` can be proved when `x` is positive.
It just means that if you are working on an intermediate step of a proof and you need the result that `sqrt y >= 0` you don't need to provide a proof that `y >= 0`. If you wanted an intermediate result that `(sqrt y) * 2 = y` then you would still need to provide a proof that `y >= 0`, though.
I'm not sure what you mean exactly? There is no soundness issue here, the fact that `sqrt -1` is defined to be 0 does not have any impact on what statements about `sqrt x` can be proved when `x` is positive.
It just means that if you are working on an intermediate step of a proof and you need the result that `sqrt y >= 0` you don't need to provide a proof that `y >= 0`. If you wanted an intermediate result that `(sqrt y) * 2 = y` then you would still need to provide a proof that `y >= 0`, though.