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Proof step 23 from proof prepost-remove (previous step)

kar[m1] = key-index(key, m), ar1[m] = elemindex(a, m1), ar = ar1[bh.ar[n].idx, ar1[bh.ar[n].idx].idx:= n], ar0 = ar1, bh = bh1.ar:= bh1.ar[n, bh1.ar[bh1.size]], bh0 = bin-heap(kar, m0), bh1 = bh0.size:= (bh0.size - 1), n = m1, 2exp-size(# kar), bh1.size < # bh1.ar, n < # bh1.ar, n < bh0.size, bh.ar[n].idx < # ar1, n < # bh.ar, heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar1, m0), key-index(key, m) ∈ keyset(kar, m0), m0 ≤ # kar, bh0.size ≥ 1 ⊦ ⟪if n ≠ 0 ∧ bh.ar[n].key < bh.ar[(n - 1) / 2].key then bin_min_heap_bubble_up#(n; bh, ar) else bin_min_heap_bubble_down#(n; bh, ar)⟫ ( bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) ∧ id-idx(ar0, ar) ∧ keyset(bh.ar, bh.size) = keyset(kar, m0) -- key-index(key, m)), # keyset(kar, m0) = 0, bh1.size = n, bh1.size = 0, keyset(kar, m0) = ∅

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

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