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Proof step 17 from proof prepost-cleanup-lpt (previous step)

# lpt3 = n1 + n0, # avol1 = n1 + n0, # lpt4 = n1 + n0, lpt3[n0] = mklp(0, m1, LP_GROUP_NODES, m2), gch = bin-heap(kar, m0), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(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(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1), key-index(0, n0) ∈ keyset(gch) ⊦ ⟪gc_heap_remove#(m2; 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 < n1 + n), m0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# lpt3 = n1 + n0, # avol1 = n1 + n0, # lpt4 = n1 + n0, lpt3[n0] = mklp(0, m1, LP_GROUP_NODES, m2), gch = bin-heap(kar, m0), keyset(bin-heap(kar, m0)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), # gc-heap(cleanup-lpt(lpt4, n0), []) ≠ 0, gc-heap(cleanup-lpt(lpt4, n0), []) ≠ ∅, m0 ≠ 0, n1 ≠ 0, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(bin-heap(kar, m0), lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []) ⊦ ⟪gc_heap_remove#(m2; 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 < n1 + n)

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ gchs ≠ ∅ → # gchs ≠ 0; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]%ne-01: ⊦ ki ∈ gchs → gchs ≠ ∅; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]