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Proof step 15 from proof heap-order-overwrite-parent-ok (previous step)

m1 / 2 = m0 + 1, kar[m0 / 2] = key-index(key3, m6), kar[m0 + 1] = key-index(key2, m5), kar[m1 + 1] = key-index(key0, m3), key0 < key1, m1 + 1 < n, m1 + 1 < # kar, m0 + 1 < n, m0 + 1 < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key2 < key1, key1 < key3, key2 < key3

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 16:
m1 / 2 = m0 + 1, kar[m1 + 1] = key-index(key0, m3), kar[m0 + 1] = key-index(key2, m5), kar[m0 / 2] = key-index(key3, m6), m0 + 1 < # kar, m0 + 1 < n, m1 + 1 < # kar, m1 + 1 < n, key0 < key1, n ≤ # kar, m0 + 1 < n ∧ m0 + 1 ≠ 0 → ¬ kar[m0 + 1].key < kar[(m0 + 1 - 1) / 2].key, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key2 < key3, key1 < key3, key2 < key1

Rule argument

pos: left 11 terms: m0 + 1

Additional information

Used terms: m0 + 1