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Proof step 1 from proof prepost-extract-min (conclusion)

bin-heap-inv(bh, ar), keyset(bh) ≠ ∅, ar0 = ar, bh0 = bh ⊦ ⟪bin_min_heap_extract_min#(; bh, ar, n)⟫ ( bin-heap-inv(bh, ar) ∧ id-idx(ar0, ar) ∧ (∃ key. key-index(key, n) ∈ keyset(bh0) ∧ keyset(bh) = keyset(bh0) -- key-index(key, n) ∧ (∀ ki. ki ∈ keyset(bh0) → ¬ ki.key < key)))

System applied rule normalize

And obtained the following new goals

Proof step 2:
ar0 = ar, bh0 = bh, bin-heap-inv(bh, ar) ⊦ ⟪bin_min_heap_extract_min#(; bh, ar, n)⟫ ( bin-heap-inv(bh, ar) ∧ id-idx(ar0, ar) ∧ (∃ key. key-index(key, n) ∈ keyset(bh0) ∧ keyset(bh) = keyset(bh0) -- key-index(key, n) ∧ (∀ ki. ki ∈ keyset(bh0) → ¬ ki.key < key))), keyset(bh) = ∅

Proof step 1 from proof prepost-extract-min (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

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