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Proof step 58 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(m0, md1, # links(m, dirs), content0), err = ESUCCESS, err0 = ESUCCESS, files = files1[inode.ino, files1[inode.ino].content:= files1[inode.ino].content[pageno, buf]], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), pageno = n0, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files), 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 ⊦ ⟪afs_check_commit#(dirs, files; err; asynced1); n := n0; if err = ESUCCESS then {asynced := false; pcache_set_status#(m, n, asynced; err, pcache)}; n := n + 1⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ m ∈ files ∧ # links(m, dirs) = files[m].nlink ∧ (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 59:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files1[m] = mkfile(m0, md1, # links(m, dirs), content0), err = ESUCCESS, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m0, md1, # links(m, dirs), content0[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 ⊦ ⟪afs_check_commit#(dirs, files1[m, mkfile(m0, md1, # links(m, dirs), content0[n0, buf])]; err; asynced1); n := n0; if err = ESUCCESS then {asynced := false; pcache_set_status#(m, n, asynced; err, pcache)}; n := n + 1⟫ ( icache-cons(icache, dirs, files1[m, files1[m].content:= files1[m].content[n0, buf]]) ∧ dcache-cons(dcache, dirs, files1[m, files1[m].content:= files1[m].content[n0, buf]]) ∧ pcache-cons(pcache, dirs, files1[m, files1[m].content:= files1[m].content[n0, buf]]) ∧ synced(dirs, icache, pcache) ∧ # links(m, dirs) = files1[m].nlink ∧ (m2 + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ (af.content:= content).nlink = af.nlink; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)