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Proof step 22 from proof prepost-cleanup-lpt (previous step)

# lpt4 = n1 + n0, # avol1 = n1 + n0, # lpt3 = n1 + n0, lpt3[n0] = mklp(0, m1, LP_GROUP_NODES, m4), lpt3[n0] = mklp(m2, m3, lpf, m4), gch = bin-heap(kar, m0), keyset(gch0) = gc-heap(lpt4, []), keyset(bin-heap(kar, m0)) = gc-heap(cleanup-lpt(lpt4, n0), []), lpt1 = lpt3, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol1, nobuffer), awbuf-inv(avol, nobuffer), bin-heap-inv(gch0, lpt4), bin-heap-inv(bin-heap(kar, m0), lpt3), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol1), synced(avol), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []) ⊦ [gc_heap_remove#(m4; gch, lpt3)] ( bin-heap-inv(gch, lpt3) ∧ id-idx(lpt1, lpt3) ∧ keyset(gch) = keyset(bin-heap(kar, m0)) -- key-index(0, n0) → ⟪lpt := lpt3[n0, lpt3[n0].flags:= LP_FREE]; lpt[n0] := mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx); freelist := freelist + n0 '; awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n := n0 + 1⟫ ( n ≤ # lpt ∧ # lpt = # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n), lpt) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n), freelist) ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n), []) ∧ bin-heap-inv(gch, lpt) ∧ # lpt < n1 + n)), # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# lpt3 = n1 + n0, # avol1 = n1 + n0, # lpt4 = n1 + n0, lpt3[n0] = mklp(0, m3, LP_GROUP_NODES, m4), gch = bin-heap(kar, m0), keyset(bin-heap(kar, m0)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), lpt1 = lpt3, # gc-heap(cleanup-lpt(lpt4, n0), []) ≠ 0, gc-heap(cleanup-lpt(lpt4, n0), []) ≠ ∅, m0 ≠ 0, n1 ≠ 0, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(bin-heap(kar, m0), lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []) ⊦ [gc_heap_remove#(m4; gch, lpt3)] ( bin-heap-inv(gch, lpt3) ∧ id-idx(lpt1, lpt3) ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0) → ⟪lpt := lpt3[n0, lpt3[n0].flags:= LP_FREE]; lpt[n0] := mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx); freelist := freelist + n0 '; awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n := n0 + 1⟫ ( n ≤ # lpt ∧ # lpt = # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n), lpt) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n), freelist) ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n), []) ∧ bin-heap-inv(gch, lpt) ∧ # lpt < n1 + n))

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)