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Proof step 17 from proof afs-cons-remove-orphans (previous step)

dirs[ino] = mkdir(m1, md0, # links(ino, dirs), m3, entries), files[ino] = mkfile(m, md, m0, content), ROOT_INO ∈ dirs, ino ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs), ∀ name0. ino ∈ dirs ∧ name0 ∈ dirs[ino].entries → dirs[ino].entries[name0] ∈ dirs ∨ dirs[ino].entries[name0] ∈ files, ∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE ⊦ ino ∈ orphans(dirs, files), (ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅) ∧ # links(ino, dirs) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs) ∧ (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 18:
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, ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅, entries[name] ∈ files ∧ ¬ entries[name] ∈ orphans(dirs, files), entries[name] ∈ dirs ∧ ¬ entries[name] ∈ orphans(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ ∅; (s)% ⊦ # ∅ = 0; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)