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Proof step 14 from proof prepost-extract-min (previous step)

bh = bin-heap(kar, m), bh0 = bin-heap(kar, m - 1), 2exp-size(# kar), 0 < # bh.ar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, m ≥ 1, ∃ key. key-index(key, bh.ar[0].idx) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key) ⊦ ⟪ar0 := ar; if bh0.size ≠ 0 then {bh0.ar[0] := bh0.ar[bh0.size]; ar[bh0.ar[0].idx].idx := 0; bin_min_heap_bubble_down#(0; bh0, ar)}⟫ ( bh0.size ≤ # bh0.ar ∧ no-dups-idx(bh0.ar, bh0.size) ∧ valid-idx(bh0.ar, ar, bh0.size) ∧ 2exp-size(# bh0.ar) ∧ heap-order(bh0.ar, bh0.size) ∧ id-idx(ar0, ar) ∧ (∃ key. key-index(key, bh.ar[0].idx) ∈ keyset(kar, m) ∧ keyset(bh0.ar, bh0.size) = keyset(kar, m) -- key-index(key, bh.ar[0].idx) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key))), # keyset(kar, m) = 0, keyset(kar, m) = ∅

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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