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Proof step 76 from proof prepost-bubble-down (previous step)

# kar0 = # kar, kar0[5 + 4 * n0] = key-index(key9, m9), kar0[n0] = key-index(key4, m4), kar0[2 * n0 + 2] = key-index(key3, m3), kar[n1] = key-index(key1, m2), kar[2 * n1 + 2] = key-index(key0, m1), kar[2 * n1 + 1] = key-index(key, m0), kar0[2 * n0 + 1] = key-index(key2, m), kar0[6 + 4 * n0] = key-index(key7, m7), keyset(kar0, n2 + n0) = keyset(kar, n2 + n0), m4 < # ar, m3 < # ar, 2 * n0 + 2 < # kar, 2 * n0 + 1 < # kar, n0 < # kar, n0 + 1 < n2, key3 < key2, n0 + 2 < n2, heap-order(kar0[n0, key-index(key3, m3)], n2 + n0), id-idx(ar1, ar), no-dups-idx(kar, n2 + n0), no-dups-idx(kar0, n2 + n0), valid-idx(kar, ar1, n2 + n0), valid-idx(kar0, ar, n2 + n0), n2 + n0 ≤ # 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), ¬ key2 < key4 ∧ ¬ key3 < key4 → heap-order(kar0, n2 + n0), key2 < key4 ∨ key3 < key4, 3 * n0 + 5 < n2 ∧ key9 < key4 ∨ 3 * n0 + 6 < n2 ∧ key7 < key4, ¬ 3 * n0 + 6 < n2 ∨ ¬ key7 < key9 ⊦ heap-order(kar0[n0, key-index(key3, m3)][2 * n0 + 2, key-index(key9, m9)], n2 + n0), ¬ key9 < key3 ∧ (3 * n0 + 6 < n2 → ¬ key7 < key9)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 2

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