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Proof step 20 from proof afs-cons-remove-orphans (previous step)

dirs[ino] = mkdir(# entries, md0, # links(ino, dirs), # subdirs(ino, dirs), entries), files[ino] = mkfile(m, md, m0, content), ROOT_INO ∈ dirs, ino ∈ dirs, name ∈ entries, # links(ino, dirs) ≤ 1, ∀ name0. name0 ∈ entries → entries[name0] ∈ dirs ∨ entries[name0] ∈ files ⊦ entries = ∅, ino ∈ files, ino ∈ orphans(dirs, files), entries[name] ∈ dirs ∧ ¬(valid-ino(entries[name], dirs, files) ∧ links(entries[name], dirs) = ∅ ∧ entries[name] ≠ ROOT_INO), entries[name] ∈ files ∧ ¬(valid-ino(entries[name], dirs, files) ∧ links(entries[name], dirs) = ∅ ∧ entries[name] ≠ ROOT_INO), ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
files[ino] = mkfile(m, md, m0, content), dirs[ino] = mkdir(# entries, md0, # links(ino, dirs), # subdirs(ino, dirs), entries), name ∈ entries, ino ∈ dirs, ROOT_INO ∈ dirs, # links(ino, dirs) ≤ 1, ∀ name0. name0 ∈ entries → entries[name0] ∈ dirs ∨ entries[name0] ∈ files ⊦ entries = ∅, ino ∈ orphans(dirs, files), ino ∈ files, entries[name] ∈ files, entries[name] ∈ dirs, ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)