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Proof step 11 from proof prepost-extract-min (previous step)

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

Heuristic symbolic execution applied rule skip right

And obtained the following new goals

Rule argument

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