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Proof step 21 from proof heap-order-overwrite-children-at (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
kar[m1 + 1] = key-index(key5, m7), kar[2 * m + 1] = key-index(key3, m5), kar[m1 / 2] = key-index(key6, m8), 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), m1 + 1 < # kar, m < # kar, m1 + 1 < n, key0 < key6, m < n, n ≤ # kar, m ≠ 0 → ¬ key < key4, 2 * m + 1 < n → ¬ key3 < key, 2 * m + 2 < n → ¬ key2 < key ⊦ m1 / 2 = m, key5 < key6

Rule argument

Additional information

Used simplifier rules: nen: ⊦ ¬ key < key0 ∧ key0 = key1 → ¬ key < key1; (forward) from specification oelem[binheap-key]% ⊦ key-index(key, m) = key-index(key0, m0) ↔ key = key0 ∧ m = m0; (ws)% ⊦ m ≠ n → kar[n, ki][m] = kar[m]; (s)