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Proof step 10 from proof afs-cons-remove-orphans (previous step)

files[ino] = mkfile(m, md, m0, content), dirs[ino] = mkdir(m1, md0, m2, m3, entries), afs-cons(dirs, files), ino ∈ dirs ⊦ (ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅) ∧ ( ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) → m2 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs)) ∧ (ino ∈ files ∧ ¬ ino ∈ orphans(dirs, files) → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ ( 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
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))

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)