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Theorem max-sum-keep-current-max

n < # ar ⊦ j + ar[n] ≤ i ∧ maximum-suffix-sum(subarray(ar, 0, n), m, j) ∧ maximum-sum(subarray(ar, 0, n), i) → maximum-sum(subarray(ar, 0, n + 1), i)

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