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Proof step 86 from proof prepost-remove (previous step)

kar[2 * m1 + 2] = key-index(key3, m5), kar[2 * m1 + 1] = key-index(key2, m4), kar[m2] = key-index(key0, m0), kar[m1] = key-index(key, m), ar1[m] = elemindex(a, m1), kar[m1, key-index(key0, m0)][(m1 - 1) / 2] = key-index(key1, m3), ar = ar1[m0, ar1[m0].idx:= m1], bh = bin-heap(kar[m1, key-index(key0, m0)], m2), #(keyset(kar, m2) ++ key-index(key0, m0)) ≠ 0, m2 ≠ m1, 2exp-size(# kar), m1 < m2, m0 < # ar1, m2 < # kar, m1 < # kar, m1 + 1 < # kar, heap-order(kar, m2 + 1), no-dups-idx(kar, m2 + 1), valid-idx(kar, ar1, m2 + 1), 2 * m1 + 1 < m2 ∧ key2 < key0 ∨ 2 * m1 + 2 < m2 ∧ key3 < key0 → heap-order(kar[m1, (2 * m1 + 2 < m2 ∧ key3 < key2 ⊃ key-index(key3, m5);key-index(key2, m4))], m2), (2 * m1 + 1 < m2 → ¬ key2 < key0) ∧ (2 * m1 + 2 < m2 → ¬ key3 < key0) → heap-order(kar[m1, key-index(key0, m0)], m2), m1 ≠ 0 → (m1 - 1) / 2 < # kar ∧ 1 ≤ m1, key-index(key, m) = key-index(key0, m0) ∨ key-index(key, m) ∈ keyset(kar, m2) ⊦ [bin_min_heap_bubble_down#(m1; bh, ar)] ( bh.size = m2 ∧ # bh.ar = # kar ∧ id-idx(ar1, ar) ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ heap-order(bh.ar, bh.size) ∧ keyset(kar[m1, key-index(key0, m0)], bh.size) = keyset(bh.ar, bh.size) → bh.size ≤ # bh.ar ∧ 2exp-size(# bh.ar) ∧ keyset(bh.ar, bh.size) = (keyset(kar, bh.size) ++ kar[bh.size]) -- key-index(key, m)), m1 ≠ 0 ∧ key0 < key1

User applied rule skip call

And obtained the following new goals

Rule argument

pos: right 1

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