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Proof step 79 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, asynced ↔ false, 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 = ESUCCESS, ino = m, key = datakey(ino, pageno), pageno = 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), key ∈ pcache, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0 ⊦ 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[key, mkpentry(asynced, pcache[key].page)], dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ synced(dirs, icache, pcache[key, mkpentry(asynced, pcache[key].page)]) ∧ (m2 + VFS_PAGE_SIZE - (n0 + 1) * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
# 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), 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 ⊦ icache-cons(icache, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]) ∧ dcache-cons(dcache, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]) ∧ pcache-cons(pcache[datakey(m, n0), mkpentry(false, buf)], dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]) ∧ synced(dirs, icache, pcache[datakey(m, n0), mkpentry(false, buf)])

Rule argument

Additional information

Used simplifier rules: ⊦ mkpentry(boolvar, buf).page = buf; (s)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ n < m → (m - n) + n = m; (s)% ⊦ m + n - n + n1 = m - n1; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)