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Proof step 1 from proof heap-order-overwrite-children-at (conclusion)

n ≤ # kar, m < n ⊦ heap-order(kar, n) ∧ (m ≠ 0 → ¬ ki.key < kar[(m - 1) / 2].key) ∧ (2 * m + 1 < n → ¬ kar[2 * m + 1].key < ki.key) ∧ (2 * m + 2 < n → ¬ kar[2 * m + 2].key < ki.key) → (¬ heap-order(kar[m, ki], n) ↔ false)

System applied rule normalize

And obtained the following new goals

Proof step 2:
m < n, heap-order(kar, n), n ≤ # kar, m ≠ 0 → ¬ ki.key < kar[(m - 1) / 2].key, 2 * m + 1 < n → ¬ kar[2 * m + 1].key < ki.key, 2 * m + 2 < n → ¬ kar[2 * m + 2].key < ki.key ⊦ ¬ heap-order(kar[m, ki], n) ↔ false

Proof step 1 from proof heap-order-overwrite-children-at (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information