[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 244 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries[str], dirs0) = m12 + 1, dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), files[m] = mkfile(m14, md8, m16, content), dirs0[m] = mkdir(# entries, md5, # links(m, dirs0), # subdirs(m, dirs0), entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries, name ∈ entries[str, entries2[str0]], m ∈ dirs0, name ∈ entries, # links(m, dirs0) ≤ 1, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, entries[name] ∈ dirs0 ∨ entries[name] ∈ files ⊦ entries[str] = ROOT_INO, entries[str] = m, entries[str] = m0, entries = ∅, m = m0, entries[str, entries2[str0]][name] ∈ files, entries[str, entries2[str0]][name] ∈ dirs0, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: name = str

Additional information

Used simplifier rules: ⊦ str ≠ str0 → (str ∈ entries[str0, ino] ↔ str ∈ entries); (s)% ⊦ str ≠ str0 → entries[str0, ino][str] = entries[str]; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ str ∈ entries[str, ino]; (s)% ⊦ entries[str, ino][str] = ino; (s) Used formulas: name = str