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Proof step 18 from proof heap-order-add-parent-key (previous step)

kar[m3 + 1] = key-index(key0, m0), kar[m1 / 2] = key-index(key, m), kar[m3 / 2] = key-index(key1, m4), m3 + 1 < # kar, key0 < key1, m1 + 1 < # kar, m3 < m1, ∀ m2. ¬ m1 < m2 ∧ m2 ≠ 0 → ¬ kar[m2].key < kar[(m2 - 1) / 2].key ⊦ m3 / 2 = m1 + 1, m3 = m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
kar[m3 / 2] = key-index(key1, m4), kar[m1 / 2] = key-index(key, m), kar[m3 + 1] = key-index(key0, m0), m3 < m1, m1 + 1 < # kar, key0 < key1, m3 + 1 < # kar, ∀ m2. ¬ m1 < m2 ∧ m2 ≠ 0 → ¬ kar[m2].key < kar[(m2 - 1) / 2].key ⊦ m3 / 2 = m1 + 1, m3 = m1

Proof step 18 from proof heap-order-add-parent-key (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information