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Proof step 28 from proof prepost-update (previous step)

kar[m1, key-index(key, m)][(m1 - 1) / 2] = key-index(key0, m2), ar[m] = elemindex(a, m1), kar[m1] = key-index(key1, m), 2exp-size(# kar), m1 < m0, m1 < # kar, key < key1, 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) = ∅, (m1 = 0 ∨ ¬ key < key0 → heap-order(kar[m1, key-index(key, m)], m0)) ∧ (m1 ≠ 0 ∧ key < key0 → heap-order(kar[m1, key-index(key0, m2)], m0))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 3

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