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Proof step 11 from proof afs-cons-remove-orphans (previous step)

files[ino] = mkfile(m, md, m0, content), dirs[ino] = mkdir(m1, md0, # links(ino, dirs), m3, entries), afs-cons(dirs, files), ino ∈ dirs ⊦ (¬ ino ∈ orphans(dirs, files) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅) ∧ (¬ ino ∈ orphans(dirs, files) → # links(ino, dirs) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs)) ∧ ( ¬ ino ∈ orphans(dirs, files) ∧ name ∈ entries → entries[name] ∈ dirs ∧ ¬ entries[name] ∈ orphans(dirs, files) ∨ entries[name] ∈ files ∧ ¬ entries[name] ∈ orphans(dirs, files))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 12:
dirs[ino] = mkdir(m1, md0, # links(ino, dirs), m3, entries), files[ino] = mkfile(m, md, m0, content), afs-cons(dirs, files), ino ∈ dirs ⊦ ino ∈ orphans(dirs, files), (¬ ino ∈ orphans(dirs, files) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅) ∧ (¬ ino ∈ orphans(dirs, files) → # links(ino, dirs) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs)) ∧ ( ¬ ino ∈ orphans(dirs, files) ∧ name ∈ entries → entries[name] ∈ dirs ∧ ¬ entries[name] ∈ orphans(dirs, files) ∨ entries[name] ∈ files ∧ ¬ entries[name] ∈ orphans(dirs, files))

Rule argument

fma: ino ∈ orphans(dirs, files)

Additional information

Used formulas: ino ∈ orphans(dirs, files)