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Proof step 7 from proof prepost-insert (previous step)

ar0 = ar, bh = bin-heap(kar, m), bh = bin-heap(kar0, m0), 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#(m0 + 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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 ⊦ ⟪skip; bh := bin-heap(kar, m); bin_min_heap_resize#(m + 1; bh); bh.ar[bh.size] := ki; ar1 := ar[ki.idx, ar[ki.idx].idx:= bh.size]; bh.size := bh.size + 1; bin_min_heap_bubble_up#(bh.size - 1; bh, ar1)⟫ ( bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar1, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) ∧ id-idx(ar, ar1) ∧ keyset(bh.ar, bh.size) = keyset(kar, m) ++ ki)

Rule argument

Additional information

Used simplifier rules: ⊦ bin-heap(kar, m) = bin-heap(kar0, m0) ↔ kar = kar0 ∧ m = m0; (ws)