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Proof step 6 from proof heap-order-overwrite-children-ok (previous step)

ki = key-index(key, m0), m1 + 1 < # kar, m < # kar, m1 + 1 < n, kar[m, ki][m1 + 1].key < kar[m, ki][m1 / 2].key, m < n, n ≤ # kar, 2 * m + 1 < n → ¬ kar[2 * m + 1].key < key, 2 * m + 2 < n → ¬ kar[2 * m + 2].key < key, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key < kar[m].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m < n, kar[m, key-index(key, m0)][m1 + 1].key < kar[m, key-index(key, m0)][m1 / 2].key, m1 + 1 < n, m < # kar, m1 + 1 < # kar, n ≤ # kar, 2 * m + 2 < n → ¬ kar[2 * m + 2].key < key, 2 * m + 1 < n → ¬ kar[2 * m + 1].key < key, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key < kar[m].key

Proof step 6 from proof heap-order-overwrite-children-ok (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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