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Proof step 35 from proof prepost-cleanup-lpt (previous step)

# lpt3 = n1 + n0, # avol1 = n1 + n0, # lpt4 = n1 + n0, lpt3[n0] = mklp(0, m2, LP_GROUP_NODES, m4), lpt2[n0] = mklp(0, m2, LP_GROUP_NODES, m5), bleb = nobuffer, keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), keyset(bin-heap(kar, m1)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), lpt = lpt0, m0 = n0, m0 < # avol, n0 < # lpt2, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(gch1, lpt2), bin-heap-inv(bin-heap(kar, m1), lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(lpt3, lpt2), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []) ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, buffered(m0) = bleb, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, n0 + 1 ≤ # lpt2 ∧ # lpt2 = # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n0 + 1), lpt2[n0, mklp(0, 0, LP_FREE, m5)]) ∧ 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(gch1) = gc-heap(cleanup-lpt(lpt4, n0 + 1), []) ∧ # lpt2 < n1 + n0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# lpt4 = n1 + n0, # avol1 = n1 + n0, # lpt3 = n1 + n0, lpt2[n0] = mklp(0, m2, LP_GROUP_NODES, m5), lpt3[n0] = mklp(0, m2, LP_GROUP_NODES, m4), keyset(gch0) = gc-heap(lpt4, []), keyset(bin-heap(kar, m1)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), n0 < # lpt2, 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(bin-heap(kar, m1), lpt3), bin-heap-inv(gch1, lpt2), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n0), lpt3), id-idx(lpt3, lpt2), synced(avol1), synced(avol), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []), # lpt2 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, keyset(gch1) = 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)), []) ∧ 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 ') ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ awbuf-inv(avol[n0, unmapped], nobuffer) ∧ 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)), lpt2[n0, mklp(0, 0, LP_FREE, m5)])

Rule argument

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ id-idx(lpt0, lpt1) → ¬ # lpt0 < # lpt1; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ n = # lpt0 ∧ id-idx(lpt0, lpt1) → (n = # lpt1 ↔ true); (ss)% ⊦ 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)