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Proof step 5 from proof prepost-insert (previous step)

ar0 = ar, bh = bin-heap(kar, m), 2exp-size(# kar), ki.idx < # ar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, ∀ ki0. ki0 ∈ keyset(kar, m) → ki0.idx ≠ ki.idx ⊦ ⟪bin_min_heap_insert#(ki; 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(ar0, ar) ∧ keyset(bh.ar, bh.size) = keyset(kar, m) ++ ki)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 6:
ar0 = ar, bh = bin-heap(kar, m), 2exp-size(# kar), ki.idx < # ar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, ∀ ki0. ki0 ∈ keyset(kar, m) → ki0.idx ≠ ki.idx ⊦ ⟪if ¬ ki.idx < # ar then abort; bin_min_heap_resize#(bh.size + 1; bh); bh.ar[bh.size] := ki; ar[ki.idx].idx := bh.size; bh.size := bh.size + 1; bin_min_heap_bubble_up#(bh.size - 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(ar0, ar) ∧ keyset(bh.ar, bh.size) = keyset(kar, m) ++ ki)

Rule argument

pos: right 1

Additional information

Used simplifier rules: bin_min_heap_insert#(ki; bh, ar) {if ¬ ki.idx < # ar then abort; bin_min_heap_resize#(bh.size + 1; bh); bh.ar[bh.size] := ki; ar[ki.idx].idx := bh.size; bh.size := bh.size + 1; bin_min_heap_bubble_up#(bh.size - 1; bh, ar) };