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Proof step 12 from proof count-i2j-max (previous step)

¬ i < max(count-i2j(i + 1, j)), i < j, ∀ j0, i0. i→n(j0 - i0) < i→n(j - i) → i0 ≤ j0 → max(count-i2j(i0, j0)) = j0 ⊦ i = j, i = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
i < j, max(count-i2j(i + 1, j)) ≤ i, max(count-i2j(i + 1, j)) < j, ∀ j0, i0. i→n(j0 - i0) < i→n(j - i) → i0 ≤ j0 → max(count-i2j(i0, j0)) = j0 ⊦ i = j

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs