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Proof step 71 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files1[m] = mkfile(m3, md, # links(m, dirs), content1), err = err0, err = ESUCCESS, n = n0, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), dcache-cons(dcache, dirs, files1), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files1), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪pcache_set_status#(m, n, false; err, pcache); n := n + 1⟫ ( icache-cons(icache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ dcache-cons(dcache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ pcache-cons(pcache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ synced(dirs, icache, pcache) ∧ (m2 + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
# buf = VFS_PAGE_SIZE, files1[m] = mkfile(m3, md, # links(m, dirs), content1), files0[m] = mkfile(m1, md0, # links(m, dirs), content), pcache[datakey(m, n0)] = mkpentry(true, buf), err = ESUCCESS, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files1), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache ⊦ ⟪pcache_set_status#(m, n0, false; err, pcache); n := n0 + 1⟫ ( icache-cons(icache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ dcache-cons(dcache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ pcache-cons(pcache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ synced(dirs, icache, pcache) ∧ (m2 + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ⌊ESUCCESS⌋ ; (s)