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Proof step 69 from proof prepost-update (previous step)

ar[m] = elemindex(a, m1), kar[m1] = key-index(key1, m), kar[m1, key-index(key, m)][(m1 - 1) / 2] = key-index(key0, m2), ar0 = ar, bh = bin-heap(kar[m1, key-index(key, m)], m0), 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, m1 = 0 ∨ ¬ key < key0 → heap-order(kar[m1, key-index(key, m)], m0), m1 ≠ 0 ∧ key < key0 → heap-order(kar[m1, kar[m1, key-index(key, m)][(m1 - 1) / 2]], m0) ⊦ [bin_min_heap_bubble_up#(m1; bh, ar)] ( bh.size = m0 ∧ # bh.ar = # kar ∧ id-idx(ar0, ar) ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ heap-order(bh.ar, bh.size) ∧ (keyset(kar, bh.size) -- kar[m1]) ++ key-index(key, m) = keyset(bh.ar, bh.size) → bh.size ≤ # bh.ar ∧ 2exp-size(# bh.ar) ∧ keyset(bh.ar, bh.size) = (keyset(kar, bh.size) -- key-index(key1, m)) ++ key-index(key, m)), # keyset(kar, m0) = 0, keyset(kar, m0) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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