[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 49 from proof crash-neutral-unlink (previous step)

# links(entries0[str], dirs0) = m0 + 1, dirs0[m] = mkdir(m1 + 1, md1, # links(m, dirs0), m2, entries0), files1[entries0[str]] = mkfile(m3, md2, m0 + 1, content), dirs = dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], mkfile(m3, md2, m0, content)], afs-cons(dirs0, files1), entries0[str] ∈ files1, str ∈ entries0, m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(entries0[str], md0, false, m0 + 1, 0, m5); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ asynced

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 50:
# links(entries0[str], dirs0) = m0 + 1, files1[entries0[str]] = mkfile(m3, md2, m0 + 1, content), dirs0[m] = mkdir(m1 + 1, md1, # links(m, dirs0), m2, entries0), dirs = dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], mkfile(m3, md2, m0, content)], inode = mkinode(entries0[str], md0, false, m0 + 1, 0, m5), afs-cons(dirs0, files1), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta; p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ asynced

Rule argument

pos: right 1

Additional information

Used simplifier rules: internal-inode-sync: ⊦ ;