There is an implicit invariant that 0 <= min, and min <= max, so max - min is between 0 and int_max inclusive, so you avoid overflowing with that calculation. To be sure that you avoid overflowing at the sum step, you need to prove that min + (max - min) / 2 <= max.
what if max is already overflown due to size of array (without even doing the lo + high calculation?) Then
min + (max- min)/2 would be min + (smaller negative value) which would violate the min + (max-min)/2 <= max
Assuming the value of max passed in is "sane" (non-negative and within array bounds), it is strictly decreasing and should never overflow.
This makes sure that none of the quantities being calculated will overflow while still returning the same answer.