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Proof step 8 from proof heap-order-pull-up-child (previous step)

kar[m, (2 * m + 2 < n ∧ kar[2 * m + 2].key < key1 ⊃ kar[2 * m + 2];kar[2 * m + 1])][m1 / 2] = key-index(key0, m2), kar[m, (2 * m + 2 < n ∧ kar[2 * m + 2].key < key1 ⊃ kar[2 * m + 2];kar[2 * m + 1])][m1 + 1] = key-index(key, m0), kar[2 * m + 1] = key-index(key1, m3), m1 + 1 < # kar, 2 * m + 1 < # kar, m < # kar, m1 + 1 < n, key < key0, 2 * m + 1 < n, m < n, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
kar[2 * m + 1] = key-index(key1, m3), kar[m, (2 * m + 2 < n ∧ kar[2 * m + 2].key < key1 ⊃ kar[2 * m + 2];key-index(key1, m3))][m1 + 1] = key-index(key, m0), kar[m, (2 * m + 2 < n ∧ kar[2 * m + 2].key < key1 ⊃ kar[2 * m + 2];key-index(key1, m3))][m1 / 2] = key-index(key0, m2), m < n, 2 * m + 1 < n, key < key0, m1 + 1 < n, m < # kar, 2 * m + 1 < # kar, m1 + 1 < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦

Proof step 8 from proof heap-order-pull-up-child (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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