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Proof step 237 from proof inv-link (previous step)

dirs[ino1] = mkdir(m1, md1, # links(ino1, dirs), m4, entries), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), dent = negdentry(p.last), err = ESUCCESS, p_ino = ino1, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md0), px(user, md1), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, parent(p), ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ files, ino0 ∈ dirs, ino1 ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ p = ε, pre-lookup(p_ino, dent, dirs, files), entries0[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 238:
dirs[ROOT_INO].nlink = 0, dirs[ino1] = mkdir(m1, md1, # links(ino1, dirs), m4, entries), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), p = p.head ', afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md0), px(user, md1), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, parent(p), ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ files, ino0 ∈ dirs, ino1 ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ino1 = ROOT_INO, p = ε, entries0[str] ∈ dirs

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) → ¬ ROOT_INO ∈ files; (s)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)% ⊦ p ≠ ε → (parent(p) = ε ↔ p = p.head '); (s)%⊦ ispath(p, ino, n, dirs, files) → (# links(n, dirs) = 0 ↔ p = ε ∧ links(ino, dirs) = ∅); (ws)% ⊦ 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)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)