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Theorem prepost-update

bin-heap-inv(bh, ar), ar0 = ar, bh0 = bh, key-index(key0, m) ∈ keyset(bh0), ar[m].idx = n ⊦ ⟪bin_min_heap_update#(n, key; bh, ar)⟫ (bin-heap-inv(bh, ar) ∧ id-idx(ar0, ar) ∧ keyset(bh) = (keyset(bh0) -- key-index(key0, m)) ++ key-index(key, m))

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