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Proof step 8 from proof suffix-upper-bound-reduce (previous step)

∀ n. n ≤ # ar → sum(ar, n, # ar - n) ≤ i, ∀ n. n ≤ # ar0 → sum(ar0, n, # ar0 - n) ≤ i0 ⊦ ∀ n. (n ≤ # ar → sum(ar, n, # ar - n) ≤ i) → n ≤ # ar0 → sum(ar0, n, # ar0 - n) ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i0 < sum(ar0, n, # ar0 - n), n ≤ # ar0, n ≤ # ar → sum(ar, n, # ar - n) ≤ i, ∀ n. n ≤ # ar0 → sum(ar0, n, # ar0 - n) ≤ i0, ∀ n. n ≤ # ar → sum(ar, n, # ar - n) ≤ i ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ↔ ¬ j < i; (ss)