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

kar[2 * n + 1] = key-index(key, m0), kar[2 * n + 2] = key-index(key0, m1), ar0 = ar, bh = bin-heap(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, (2 * n + 1 < m → ¬ key < kar[n].key) ∧ (2 * n + 2 < m → ¬ key0 < kar[n].key) → heap-order(kar, m), 2 * n + 1 < m ∧ key < kar[n].key ∨ 2 * n + 2 < m ∧ key0 < kar[n].key → heap-order(kar[n, (2 * n + 2 < m ∧ key0 < key ⊃ kar[2 * n + 2];key-index(key, m0))], m) ⊦ ⟪bin_min_heap_bubble_down#(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

Rule argument

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