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Proof step 79 from proof prepost-update (previous step)

kar[m1] = key-index(key1, m), ar[m] = elemindex(a, m1), kar[2 * m1 + 2] = key-index(key0, m2), kar[2 * m1 + 1] = key-index(key2, m3), 2exp-size(# kar), m1 < m0, m1 < # kar, heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), key-index(key1, m) ∈ keyset(kar, m0), m0 ≤ # kar ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅, key < key1, ((2 * m1 + 1 < m0 → ¬ key2 < key) ∧ (2 * m1 + 2 < m0 → ¬ key0 < key) → heap-order(kar[m1, key-index(key, m)], m0)) ∧ ( 2 * m1 + 1 < m0 ∧ key2 < key ∨ 2 * m1 + 2 < m0 ∧ key0 < key → heap-order(kar[m1, (2 * m1 + 2 < m0 ∧ key0 < key2 ⊃ key-index(key0, m2);kar[2 * m1 + 1])], m0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
kar[2 * m1 + 1] = key-index(key2, m3), kar[2 * m1 + 2] = key-index(key0, m2), ar[m] = elemindex(a, m1), kar[m1] = key-index(key1, m), 2exp-size(# kar), m1 < # kar, m1 < m0, heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), key-index(key1, m) ∈ keyset(kar, m0), m0 ≤ # kar ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅, key < key1, ((2 * m1 + 1 < m0 → ¬ key2 < key) ∧ (2 * m1 + 2 < m0 → ¬ key0 < key) → heap-order(kar[m1, key-index(key, m)], m0)) ∧ ( 2 * m1 + 1 < m0 ∧ key2 < key ∨ 2 * m1 + 2 < m0 ∧ key0 < key → heap-order(kar[m1, (2 * m1 + 2 < m0 ∧ key0 < key2 ⊃ key-index(key0, m2);key-index(key2, m3))], m0))

Proof step 79 from proof prepost-update (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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