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Proof step 119 from proof prepost-bubble-down (previous step)

# kar0 = # kar, kar0[2 * n0 + 2] = key-index(key2, m), kar[n1] = key-index(key1, m2), kar[2 * n1 + 2] = key-index(key0, m1), kar[2 * n1 + 1] = key-index(key, m0), kar0[n0] = key-index(key3, m3), kar0[4 + 4 * n0] = key-index(key4, m4), kar0[3 + 4 * n0] = key-index(key5, m5), kar0[2 * n0 + 1] = key-index(key6, m6), keyset(kar0, n2 + n0) = keyset(kar, n2 + n0), n0 + 1 < n2, m6 < # ar, m3 < # ar, 2 * n0 + 1 < # kar, n0 < # kar, heap-order(kar0[n0, key-index(key6, m6)], n2 + n0), id-idx(ar1, ar), no-dups-idx(kar0, n2 + n0), no-dups-idx(kar, n2 + n0), valid-idx(kar0, ar, n2 + n0), valid-idx(kar, ar1, n2 + n0), n2 + n0 ≤ # kar, ¬ key6 < key3 ∧ (n0 + 2 < n2 → ¬ key2 < key3) → heap-order(kar0, n2 + n0), n0 + 2 < n2 → 2 * n0 + 2 < # kar, 2 * n1 + 1 < n2 + n0 ∧ key < key1 ∨ 2 * n1 + 2 < n2 + n0 ∧ key0 < key1 → heap-order(kar[n1, (2 * n1 + 2 < n2 + n0 ∧ key0 < key ⊃ key-index(key0, m1);key-index(key, m0))], n2 + n0), (2 * n1 + 1 < n2 + n0 → ¬ key < key1) ∧ (2 * n1 + 2 < n2 + n0 → ¬ key0 < key1) → heap-order(kar, n2 + n0), key6 < key3 ∨ n0 + 2 < n2 ∧ key2 < key3 ⊦ no-dups-idx(kar0[n0, key-index(key6, m6)][2 * n0 + 1, key-index(key3, m3)], n2 + n0), n0 + 2 < n2 ∧ key2 < key6

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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