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Proof step 20 from proof max-sum-new-current-max (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: n1, 0 abort: F discard: F computed: F

Additional information

Used simplifier rules: sum-zero: ⊦ sum(ar, n, 0) = 0;% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: n1, 0