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Proof step 16 from proof heap-order-overwrite-children-at (previous step)

kar[m1 + 1] = key-index(key5, m7), kar[2 * m + 1] = key-index(key3, m5), kar[m, key-index(key, m0)][m1 / 2] = key-index(key1, m3), kar[m, key-index(key, m0)][m1 + 1] = key-index(key0, m2), kar[2 * m + 2] = key-index(key2, m4), kar[(m - 1) / 2] = key-index(key4, m6), kar[m1 / 2] = key-index(key6, m8), m1 + 1 < # kar, m < # kar, m1 + 1 < n, key0 < key1, m < n, n ≤ # kar, m ≠ 0 → ¬ key < key4, 2 * m + 1 < n → ¬ key3 < key, 2 * m + 2 < n → ¬ key2 < key ⊦ key5 < key6

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 17:
m1 / 2 = m, kar[m1 / 2] = key-index(key6, m8), kar[(m - 1) / 2] = key-index(key4, m6), kar[2 * m + 2] = key-index(key2, m4), kar[m, key-index(key, m0)][m1 + 1] = key-index(key0, m2), kar[m, key-index(key, m0)][m1 / 2] = key-index(key1, m3), kar[2 * m + 1] = key-index(key3, m5), kar[m1 + 1] = key-index(key5, m7), m < n, key0 < key1, m1 + 1 < n, m < # kar, m1 + 1 < # kar, n ≤ # kar, 2 * m + 2 < n → ¬ key2 < key, 2 * m + 1 < n → ¬ key3 < key, m ≠ 0 → ¬ key < key4 ⊦ key5 < key6
Proof step 21:
kar[m1 / 2] = key-index(key6, m8), kar[(m - 1) / 2] = key-index(key4, m6), kar[2 * m + 2] = key-index(key2, m4), kar[m, key-index(key, m0)][m1 + 1] = key-index(key0, m2), kar[m, key-index(key, m0)][m1 / 2] = key-index(key1, m3), kar[2 * m + 1] = key-index(key3, m5), kar[m1 + 1] = key-index(key5, m7), m < n, key0 < key1, m1 + 1 < n, m < # kar, m1 + 1 < # kar, n ≤ # kar, 2 * m + 2 < n → ¬ key2 < key, 2 * m + 1 < n → ¬ key3 < key, m ≠ 0 → ¬ key < key4 ⊦ m1 / 2 = m, key5 < key6

Rule argument

fma: m1 / 2 = m

Additional information

Used formulas: m1 / 2 = m