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Proof step 1 from proof prepost-update (conclusion)

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))

System applied rule normalize

And obtained the following new goals

Proof step 2:
ar[m].idx = n, ar0 = ar, bh0 = bh, bin-heap-inv(bh, ar), key-index(key0, m) ∈ keyset(bh0) ⊦ ⟪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))

Proof step 1 from proof prepost-update (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information