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Proof step 8 from proof prepost-cleanup-lpt (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# avol1 = # lpt4, # lpt3 = # lpt4, lpt3[n0].flags = LP_GROUP_NODES, lpt3[n0].ref-size = 0, keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), n0 < # lpt4, 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(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol1), synced(avol) ⊦ ⟪gc_heap_remove#(lpt3[n0].gcheapidx; gch, lpt3); 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 < (# lpt4 - n0) + n)

Rule argument

Additional information

Used simplifier rules: elim-lp-upd-size: ⊦ lp.size:= n = mklp(lp.ref-size, n, lp.flags, lp.gcheapidx);% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ awbuf-inv(avol, nobuffer) → (synced(avol) ↔ true); (ss)% ⊦ nx + n = nx + n '; (s)%⊦ id-idx(lpt0, lpt1) → (freelist-cons(lpt1, freelist) ↔ freelist-cons(lpt0, freelist)); (s)% ⊦ m < n → m ≤ n; (s)