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Proof step 243 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries[str], dirs0) = m12 + 1, dirs0[ino] = mkdir(# entries4, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries4), files[ino] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), ino = m, mkdir(m8, md1, # links(m, dirs0), m11, entries[str, entries2[str0]]) = mkdir(m20, md10, m21, m22, entries5), afs-cons(dirs0, files), ino ∈ dirs0, name ∈ entries5, m ∈ dirs0, str ∈ entries, entries2[str0] ∈ dirs0, str0 ∈ entries2, m0 ∈ dirs0, entries[str] ∈ dirs0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries4 = ∅, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries[str] = m0, entries[str] = m, entries[str] = ROOT_INO, ino = entries[str], m = m0, entries5[name] ∈ dirs0, entries5[name] ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 244:
# links(entries[str], dirs0) = m12 + 1, dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), files[m] = mkfile(m14, md8, m16, content), dirs0[m] = mkdir(# entries, md5, # links(m, dirs0), # subdirs(m, dirs0), entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries, name ∈ entries[str, entries2[str0]], m ∈ dirs0, name ∈ entries, # links(m, dirs0) ≤ 1, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, entries[name] ∈ dirs0 ∨ entries[name] ∈ files ⊦ entries[str] = ROOT_INO, entries[str] = m, entries[str] = m0, entries = ∅, m = m0, entries[str, entries2[str0]][name] ∈ files, entries[str, entries2[str0]][name] ∈ dirs0, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ ∅; (s)% ⊦ # ∅ = 0; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ str = str0 → entries[str0, ino][str] = ino; (s)% ⊦ str ∈ entries[str0, ino] ↔ str = str0 ∨ str ∈ entries; (ws)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)