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Proof step 10 from proof max-sum-next-less-zero (previous step)

n1 + m0 = n + 1, sum(ar, n0, m) < sum(ar, n1, m0), ar[n] < 0, n0 + m < # ar, n < # ar, n0 + m ≤ n, n0 + m ≤ n + 1, ∀ n2, m1. n2 + m1 ≤ n → sum(ar, n2, m1) ≤ sum(ar, n0, m) ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 11:
n1 + m0 = n + 1, m0 = 0, n < # ar, n0 + m < # ar, ar[n] < 0, sum(ar, n0, m) < sum(ar, n1, m0), n0 + m ≤ n + 1, n0 + m ≤ n, ∀ n2, m1. n2 + m1 ≤ n → sum(ar, n2, m1) ≤ sum(ar, n0, m) ⊦
Proof step 13:
n1 + m0 = n + 1, n < # ar, n0 + m < # ar, ar[n] < 0, sum(ar, n0, m) < sum(ar, n1, m0), n0 + m ≤ n + 1, n0 + m ≤ n, ∀ n2, m1. n2 + m1 ≤ n → sum(ar, n2, m1) ≤ sum(ar, n0, m) ⊦ m0 = 0

Rule argument

fma: m0 = 0

Additional information

Used formulas: m0 = 0