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Proof step 76 from proof prepost-cleanup-lpt (previous step)

# lpt3 = n2 + n0, # avol1 = n2 + n0, # lpt4 = n2 + n0, lpt3[n0] = mklp(m0, m1, lpf, m2), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), m0 = 0, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(gch, lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1) ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n1 := n0 + 1⟫ ( n1 ≤ # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n1), lpt3[n0, mklp(m0, 0, LP_FREE, m2)]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n1), freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n1), []) ∧ bin-heap-inv(gch, lpt3[n0, mklp(m0, 0, LP_FREE, m2)]) ∧ # lpt4 < n2 + n1), lpf = LP_GROUP_NODES, lpf = LP_FREE, n2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
# lpt4 = n2 + n0, # avol1 = n2 + n0, # lpt3 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), lpf ≠ LP_FREE, lpf ≠ LP_GROUP_NODES, n2 ≠ 0, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol1, nobuffer), awbuf-inv(avol, nobuffer), bin-heap-inv(gch0, lpt4), bin-heap-inv(gch, lpt3), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol1), synced(avol) ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n1 := n0 + 1⟫ ( n1 ≤ # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n1), lpt3[n0, mklp(0, 0, LP_FREE, m2)]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n1), freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n1), []) ∧ # lpt4 < n2 + n1)

Rule argument

Additional information

Used simplifier rules: n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, m2)]) ↔ bin-heap-inv(gch, lpt)); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)