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Proof step 8 from proof prepost-bubble-up (previous step)

kar[n] = key-index(key, m0), kar[(n - 1) / 2] = key-index(key0, m1), ar0 = ar, bh = bin-heap(kar, m), n < m, n < # kar, no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, n = 0 ∨ ¬ key < key0 → heap-order(kar, m), n ≠ 0 ∧ key < key0 → heap-order(kar[n, kar[(n - 1) / 2]], m) ⊦ ⟪bin_min_heap_bubble_up#(n; bh, ar)⟫ ( bh.size = m ∧ # bh.ar = # kar ∧ id-idx(ar0, ar) ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ heap-order(bh.ar, bh.size) ∧ keyset(kar, bh.size) = keyset(bh.ar, bh.size))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
kar[(n - 1) / 2] = key-index(key0, m1), kar[n] = key-index(key, m0), ar0 = ar, bh = bin-heap(kar, m), n < # kar, n < m, no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, n ≠ 0 ∧ key < key0 → heap-order(kar[n, key-index(key0, m1)], m), n = 0 ∨ ¬ key < key0 → heap-order(kar, m) ⊦ ⟪bin_min_heap_bubble_up#(n; bh, ar)⟫ ( bh.size = m ∧ # bh.ar = # kar ∧ id-idx(ar0, ar) ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ heap-order(bh.ar, bh.size) ∧ keyset(kar, bh.size) = keyset(bh.ar, bh.size))

Proof step 8 from proof prepost-bubble-up (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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