One case missing in the code written

I think in this code(shown in video of maximum subarray 2),a case is being missed. We consider all the cases of differences of cumulative sum.But we should also consider the case of comparision of current sum with the cumulative sum alone as it also indicates the subarray as well.Those cases are being missed in the video.Correct me,if i am wrong.

What you are saying is cum[I]-ar[I] should be considered?
Won’t that be equal to cum[I]-cum[i-1]
We have considered all cases

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