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Thanks - I was not aware that theorem provers often allow "division" by zero. Looking at https://xenaproject.wordpress.com/2020/07/05/division-by-zero-in-type-

Thanks - I was not aware that theorem provers often allow "division" by zero. Looking at https://xenaproject.wordpress.com/2020/07/05/division-by-zero-in-type-theory-a-faq/ https://xenaproject.wordpress.com/2020/07/05/division-by-zer... I see that they don't use mathematical division, but define a slightly different operator with an additional condition for handling zero. This appears to be far more convenient for theorem provers. The trade-off would be that "division" is no longer the inverse of multiplication.

momentoftop 4y ago
Ah, thanks for the link. I suggested the reason that Isabelle/HOL does this is because it requires total functions and you don't have a convenient way to do refinement types. But that's not an adequate explanation, because Lean does allow such refinements, but it still turns out to be inconvenient for division. I will note that setting a - b = 0 for a <= b is pretty standard, and is often called "partial subtraction."