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Proof step 10 from proof heap-order-overwrite0 (previous step)

kar[0, key-index(key, m1)][m0 / 2] = key-index(key1, m3), kar[m0 + 1] = key-index(key0, m2), kar[0] = key-index(key2, m4), m0 + 1 < # kar, m0 + 1 < n, key0 < key1, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key2 < key

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 11:
m0 / 2 = 0, kar[0] = key-index(key2, m4), kar[m0 + 1] = key-index(key0, m2), kar[0, key-index(key, m1)][m0 / 2] = key-index(key1, m3), key0 < key1, m0 + 1 < n, m0 + 1 < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key2 < key
Proof step 17:
kar[0] = key-index(key2, m4), kar[m0 + 1] = key-index(key0, m2), kar[0, key-index(key, m1)][m0 / 2] = key-index(key1, m3), key0 < key1, m0 + 1 < n, m0 + 1 < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m0 / 2 = 0, key2 < key

Rule argument

fma: m0 / 2 = 0

Additional information

Used formulas: m0 / 2 = 0