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Proof step 8 from proof heap-order-overwrite-parent-ok (previous step)

ki = key-index(key, m2), m0 + 1 < # kar, m1 + 1 < # kar, m1 + 1 < n, kar[m0 + 1, ki][m1 + 1].key < kar[m0 + 1, ki][m1 / 2].key, m0 + 1 < n, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ kar[m0 + 1].key < kar[m0 / 2].key, key < kar[m0 / 2].key, kar[m0 + 1].key < key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
m0 + 1 < n, kar[m0 + 1, key-index(key, m2)][m1 + 1].key < kar[m0 + 1, key-index(key, m2)][m1 / 2].key, m1 + 1 < n, m1 + 1 < # kar, m0 + 1 < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ kar[m0 + 1].key < key, key < kar[m0 / 2].key, kar[m0 + 1].key < kar[m0 / 2].key

Proof step 8 from proof heap-order-overwrite-parent-ok (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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