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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
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, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ key1 < key3, key2 < key1, key2 < key3

Rule argument

Additional information

Used simplifier rules: ⊦ key-index(key, m).key = key; (s)% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)