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Proof step 1 from proof upper-bound-reduce (conclusion)

⊦ upper-bound(ar, i) → (upper-bound(ar0, i0) ↔ (∀ n, m. (n + m ≤ # ar → sum(ar, n, m) ≤ i) → n + m ≤ # ar0 → sum(ar0, n, m) ≤ i0))

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information