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

kar[m0] = key-index(key2, m4), kar[2 * m0 + 1] = key-index(key4, m6), kar[2 * m0 + 2] = key-index(key3, m5), kar[m1 + 1] = key-index(key0, m2), m1 = m0 * 2 + n0, m1 + 1 < # kar, m1 + 1 < n, key0 < key1, m0 < n, m0 < # kar, n0 < 2, n ≤ # kar, 2 * m0 + 1 < n → ¬ key4 < key1, 2 * m0 + 2 < n → ¬ key3 < key1, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ 2 = 0, key1 < key2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
kar[m0] = key-index(key2, m4), kar[2 * m0 + 1] = key-index(key4, m6), kar[2 * m0 + 2] = key-index(key3, m5), kar[(m0 * 2 + n0) + 1] = key-index(key0, m2), (m0 * 2 + n0) + 1 < # kar, m0 < # kar, (m0 * 2 + n0) + 1 < n, key0 < key1, m0 < n, n0 < 2, 2 * m0 + 1 < n, 2 * m0 + 1 < # kar, n ≤ # kar, 2 * m0 + 2 < n → ¬ key3 < key1, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key1 < key2, key4 < key1, key4 < key2

Rule argument

Additional information

Used simplifier rules: nnn: ⊦ ¬ key < key0 ∧ ¬ key1 < key → ¬ key1 < key0; (forward) from specification oelem[binheap-key]%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m < n → ¬ m + m0 < n; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat