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Proof step 41 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), lpt4[n0] = mklp(0, m2, LP_GROUP_NODES, m3), 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, []), n0 < # 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), []), # lpt2 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, freelist-cons(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], freelist + n0 ') ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ awbuf-inv(avol[n0, unmapped], nobuffer) ∧ id-idx(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], lpt2[n0, mklp(0, 0, LP_FREE, m5)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ bleb ≠ buffered(n) ∧ awbuf-inv(avol, bleb) → awbuf-inv(avol[n, unmapped], bleb)
Proof step 43:
# lpt4 = n1 + n0, # avol1 = n1 + n0, # lpt3 = n1 + n0, lpt4[n0] = mklp(0, m2, LP_GROUP_NODES, m3), 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, nobuffer = buffered(n0), freelist-cons(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], freelist + n0 ') ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ true ∧ id-idx(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], lpt2[n0, mklp(0, 0, LP_FREE, m5)])

Rule argument

spec: awbuf-inv name: inv-unmap seq: ⊦ bleb ≠ buffered(n) ∧ awbuf-inv(avol, bleb) → awbuf-inv(avol[n, unmapped], bleb) subst: [bleb, n, avol] → [nobuffer, n0, avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ nobuffer ≠ buffered(m); (s) Used terms: nobuffer, n0, avol