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Proof step 17 from proof inv-evict (previous step)

0 = m6, files[ino] = mkfile(m0, md, m1, content), dirs[ino] = mkdir(m2, md0, m3, m4, entries), dirs[m] = mkdir(m5, md1, m6, m7, entries0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino ∈ dirs → m3 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅ ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- m) = ∅ → entries = ∅) ∧ ( ino ≠ m ∧ ino ∈ dirs → m3 = # links(ino, dirs -- m) ∧ # links(ino, dirs -- m) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, dirs -- m)) ∧ (ino ∈ files → (ino = m ∨ ¬ ino ∈ dirs) ∧ m1 = # links(ino, dirs -- m)) ∧ (ino ≠ m ∧ ino ∈ dirs ∧ name ∈ entries → entries[name] ≠ m ∧ entries[name] ∈ dirs ∨ entries[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# links(m, dirs) = 0, files[ino] = mkfile(m0, md, m1, content), dirs[ino] = mkdir(m2, md0, m3, m4, entries), dirs[m] = mkdir(m5, md1, 0, m7, entries0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino ∈ dirs → m3 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅ ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- m) = ∅ → entries = ∅) ∧ ( ino ≠ m ∧ ino ∈ dirs → m3 = # links(ino, dirs -- m) ∧ # links(ino, dirs -- m) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, dirs -- m)) ∧ (ino ∈ files → (ino = m ∨ ¬ ino ∈ dirs) ∧ m1 = # links(ino, dirs -- m)) ∧ (ino ≠ m ∧ ino ∈ dirs ∧ name ∈ entries → entries[name] ≠ m ∧ entries[name] ∈ dirs ∨ entries[name] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%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