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Proof step 111 from proof prepost-cleanup-lpt (previous step)

# lpt = # lpt4, # avol1 = # lpt4, isbuf ↔ boolvar, avol0 = avol1, bleb = nobuffer, keyset(gch) = gc-heap(cleanup-lpt(lpt4, n), []), keyset(gch0) = gc-heap(lpt4, []), lpt = lpt3, lpt0 = lpt1, lpt2 = lpt4, m = m0, n = n0, n1 = 0, n < # lpt, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, bleb), awbuf-inv(avol1, nobuffer), bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt4), freelist-cons(lpt, freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n), lpt), synced(avol), synced(avol1), n ≤ # lpt, lpt[n].ref-size = 0 → n < # lpt ⊦ lpt[n].ref-size = 0 ∧ lpt[n].flags ≠ LP_FREE, ( n + 1 ≤ # lpt ∧ # lpt = # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n + 1), lpt) ∧ awbuf-inv(avol, bleb) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(lpt, freelist) ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n + 1), []) ∧ bin-heap-inv(gch, lpt) ∧ bleb = nobuffer ∧ synced(avol)) ∧ # lpt - n + 1 < # lpt3 - n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 112:
# lpt3 = # lpt4, # avol1 = # lpt4, keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # lpt4, 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) ⊦ 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) ∧ 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) ∧ 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)), []), lpt3[n0].ref-size = 0 ∧ lpt3[n0].flags ≠ LP_FREE

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ n < m → (m - n) + n = m; (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ awbuf-inv(avol, nobuffer) → (synced(avol) ↔ true); (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ n < m → m - n ≠ 0; (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)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ 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)%⊦ id-idx(lpt0, lpt1) → (freelist-cons(lpt1, freelist) ↔ freelist-cons(lpt0, freelist)); (s)% ⊦ m < n → m ≤ n; (s)