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Proof step 5 from proof prepost-get-min (previous step)

# keyset(kar, m) ≠ 0, keyset(kar, m) ≠ ∅, 2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ ⟪bin_min_heap_get_min#(bin-heap(kar, m); n)⟫ ∃ key. key-index(key, n) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key)

Heuristic weak unfold applied rule call right

And obtained the following new goals

Proof step 6:
bh = bin-heap(kar, m), 2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ ⟪if bh.size = 0 then abort; n := bh.ar[0].idx⟫ ∃ key. key-index(key, n) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key), # keyset(kar, m) = 0, keyset(kar, m) = ∅

Rule argument

pos: right 1

Additional information

Used simplifier rules: bin_min_heap_get_min#(bh; n) {if bh.size = 0 then abort; n := bh.ar[0].idx};