[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 61 from proof crash-neutral-link (previous step)

dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries[str], dirs0[ino1] = mkdir(m4, md3, # links(ino1, dirs0), m6, entries0), dirs0[m] = mkdir(m1, md2, # links(m, dirs0), m5, entries1), files1[entries[str]] = mkfile(m0, md4, # links(entries[str], dirs0), content0), afs-cons(dirs0, files1), str ∈ entries0, str ∈ entries, ino0 ∈ dirs0, entries[str] ∈ files1, ino1 ∈ dirs0, m ∈ dirs0, ¬ entries[str] ∈ dirs0, ¬ str0 ∈ entries1, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ asynced, ⟨let ino = entries[str] in {files := files1[entries[str], mkfile(m0, md4, # links(entries[str], dirs0) + 1, content0)]; dirs := dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m5, entries1[str0, entries[str]])]; if ino ∈ files then {files[ino].size := m11; files[ino].meta := md5} else if ino ∈ dirs then dirs[ino].meta := md5}; 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 := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files))

User applied rule exists right

And obtained the following new goals

Proof step 62:
files1[entries[str]] = mkfile(m0, md4, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m1, md2, # links(m, dirs0), m5, entries1), dirs0[ino1] = mkdir(m4, md3, # links(ino1, dirs0), m6, entries0), entries0[str] = entries[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), afs-cons(dirs0, files1), m ∈ dirs0, ino1 ∈ dirs0, entries[str] ∈ files1, ino0 ∈ dirs0, str ∈ entries, str ∈ entries0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⌊EFAIL⌋ ∧ ⟨err := EFAIL; asynced := ?⟩ asynced, ⟨let ino = entries[str] in {files := files1[entries[str], mkfile(m0, md4, # links(entries[str], dirs0) + 1, content0)]; dirs := dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m5, entries1[str0, entries[str]])]; if ino ∈ files then {files[ino].size := m11; files[ino].meta := md5} else if ino ∈ dirs then dirs[ino].meta := md5}; 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 := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), entries[str] ∈ dirs0, str0 ∈ entries1

Rule argument

pos: right 1 terms: EFAIL abort: F discard: T computed: T

Additional information

Used terms: EFAIL