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Proof step 81 from proof prepost-cleanup-lpt (previous step)

# lpt4 = n2 + n0, # avol1 = n2 + n0, # lpt3 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), bleb = nobuffer, keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), lpt = lpt0, m0 = n0, m0 < # avol, 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) ⊦ buffered(m0) = bleb, lpf = LP_GROUP_NODES, lpf = LP_FREE, n2 = 0, n0 + 1 ≤ # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n0 + 1), lpt3[n0, mklp(0, 0, LP_FREE, m2)]) ∧ awbuf-inv(avol[m0, unmapped], nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol[m0, unmapped], lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n0 + 1), freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0 + 1), []) ∧ # lpt4 < n2 + n0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 82:
# 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), []), n0 < # avol, 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) ⊦ lpf = LP_GROUP_NODES, lpf = LP_FREE, n2 = 0, id-idx ((lpt4[n0].ref-size = 0 ∧ lpt4[n0].flags ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, lpt4[n0].gcheapidx)];cleanup-lpt(lpt4, n0)), lpt3[n0, mklp(0, 0, LP_FREE, m2)]) ∧ awbuf-inv(avol[n0, unmapped], nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ freelist-cons ((lpt4[n0].ref-size = 0 ∧ lpt4[n0].flags ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, lpt4[n0].gcheapidx)];cleanup-lpt(lpt4, n0)), freelist + n0 ') ∧ keyset(gch) = gc-heap ((lpt4[n0].ref-size = 0 ∧ lpt4[n0].flags ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, lpt4[n0].gcheapidx)];cleanup-lpt(lpt4, n0)), [])

Rule argument

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);% ⊦ ¬ n < n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)%n < # lpt ⊦ cleanup-lpt(lpt, n + 1) = (lpt[n].ref-size = 0 ∧ lpt[n].flags ≠ LP_FREE ⊃ cleanup-lpt(lpt, n)[n, mklp(0, 0, LP_FREE, lpt[n].gcheapidx)] ;cleanup-lpt(lpt, n) ); (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ nobuffer ≠ buffered(m); (s)