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Proof step 33 from proof prepost-remove (previous step)

kar[m2 / 2] = key-index(key1, m3), kar[m2 + 1] = key-index(key, m), ar1[m] = elemindex(a, m2 + 1), kar[m1] = key-index(key0, m0), ar = ar1[m0, ar1[m0].idx:= (m2 + 1)], bh = bin-heap(kar[m2 + 1, key-index(key0, m0)], m1), #(keyset(kar, m1) ++ key-index(key0, m0)) ≠ 0, # kar ≠ 1, m1 ≠ m2 + 1, 2exp-size(# kar), 2 + m2 < # kar, m2 + 1 < m1, m2 < # kar, m2 < m1, m0 < # ar1, m1 < # kar, m2 + 1 < # kar, key0 < key1, m2 / 2 < # kar, heap-order(kar, m1 + 1), no-dups-idx(kar, m1 + 1), valid-idx(kar, ar1, m1 + 1), key-index(key, m) = key-index(key0, m0) ∨ key-index(key, m) ∈ keyset(kar, m1) ⊦ ⟪bin_min_heap_bubble_up#(m2 + 1; bh, ar)⟫ ( bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) ∧ id-idx(ar1, ar) ∧ keyset(bh.ar, bh.size) = (keyset(kar, m1) ++ kar[m1]) -- key-index(key, m))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: prepost-bubble-up seq: bh0 = bh, ar0 = ar, bubble-up-inv(n, bh, ar, bh0, ar0) ⊦ ⟪bin_min_heap_bubble_up#(n; bh, ar)⟫ ( bh.size = bh0.size ∧ # bh.ar = # bh0.ar ∧ 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(bh0) = keyset(bh)) subst: [n, ar, bh, bh0, ar0] → [m2 + 1, ar, bh, bh, ar] flags: <all paths>

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