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Proof step 238 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries0[str], dirs0) = m12 + 1, # entries0 = m8 + 1, # subdirs(m0, dirs0) = m11 + 1, dirs0[entries0[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries0[str0]] = mkdir(m4, md3, # links(entries0[str0], dirs0), m7, entries1), files[m0] = mkfile(m14, md8, m16, content), dirs0[m0] = mkdir(m8 + 1, md5, # links(m0, dirs0), m11 + 1, entries0), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries0[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, str ∈ entries0, name ∈ (entries0 -- str0)[str, entries0[str0]], # links(m0, dirs0) ≤ 1, name ∈ entries0 → entries0[name] ∈ dirs0 ∨ entries0[name] ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m0, entries0 = ∅, mkdentry(str, entries0[str]) = mkdentry(str0, entries0[str0]), name = str, (entries0 -- str0)[str, entries0[str0]][name] ∈ files, (entries0 -- str0)[str, entries0[str0]][name] ∈ dirs0, m0 ≠ ROOT_INO ∧ links(m0, dirs0) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 239:
# subdirs(m0, dirs0) = m11 + 1, # entries0 = m8 + 1, # links(entries0[str], dirs0) = m12 + 1, dirs0[m0] = mkdir(m8 + 1, md5, # links(m0, dirs0), m11 + 1, entries0), files[m0] = mkfile(m14, md8, m16, content), dirs0[entries0[str0]] = mkdir(m4, md3, # links(entries0[str0], dirs0), m7, entries1), dirs0[entries0[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), afs-cons(dirs0, files), str ∈ entries0, entries0[str0] ∈ dirs0, str0 ∈ entries0, m0 ∈ dirs0, entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, name ∈ entries0, entries0[name] ∈ files, # links(m0, dirs0) ≤ 1, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries0[str] = m0, entries0[str] = ROOT_INO, entries0 = ∅, mkdentry(str, entries0[str]) = mkdentry(str0, entries0[str0]), (entries0 -- str0)[str, entries0[str0]][name] ∈ files, entries0[name] ∈ dirs0, m0 ≠ ROOT_INO ∧ links(m0, dirs0) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ str ≠ str0 → (entries -- str0)[str] = entries[str]; (s)% ⊦ str ≠ str0 → entries[str0, ino][str] = entries[str]; (s)% ⊦ str ∈ entries -- str0 ↔ str ≠ str0 ∧ str ∈ entries; (s)% ⊦ str ≠ str0 → (str ∈ entries[str0, ino] ↔ str ∈ entries); (s)