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Proof step 14 from proof upper-bound-reduce (previous step)

i0 < sum(ar0, n, m), i < sum(ar, n, m), n + m ≤ # ar0, n + m ≤ # ar, ∀ n, m. (n + m ≤ # ar → sum(ar, n, m) ≤ i) → n + m ≤ # ar0 → sum(ar0, n, m) ≤ i0, ∀ n, m. n + m ≤ # ar → sum(ar, n, m) ≤ i ⊦

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: n, m

Additional information

Used simplifier rules: ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: n, m