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Proof step 179 from proof afs-cons-rename-dir-negdentry (previous step)

# entries3 = m4 + 1, # subdirs(m, dirs0) = m7 + 1, dirs0[entries3[str]] = mkdir(m3, md4, # links(entries3[str], dirs0), m5, entries1), dirs0[m] = mkdir(m4 + 1, md5, # links(m, dirs0), m7 + 1, entries3), files[m] = mkfile(m9, md2, m11, content), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries3, entries3[str] ∈ dirs0, ROOT_INO ∈ dirs0, name ∈ (entries3 -- str)[str0, entries3[str]], # links(m, dirs0) ≤ 1, name ∈ entries3 → entries3[name] ∈ dirs0 ∨ entries3[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries3 = ∅, name = str0, (entries3 -- str)[str0, entries3[str]][name] ∈ files, (entries3 -- str)[str0, entries3[str]][name] ∈ dirs0, str0 ∈ entries3, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 180:
# subdirs(m, dirs0) = m7 + 1, # entries3 = m4 + 1, files[m] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m4 + 1, md5, # links(m, dirs0), m7 + 1, entries3), dirs0[entries3[str]] = mkdir(m3, md4, # links(entries3[str], dirs0), m5, entries1), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries3[str] ∈ dirs0, str ∈ entries3, m ∈ dirs0, name ∈ entries3, # links(m, dirs0) ≤ 1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, entries3[name] ∈ dirs0 ∨ entries3[name] ∈ files ⊦ entries3 = ∅, name = str, str0 ∈ entries3, (entries3 -- str)[str0, entries3[str]][name] ∈ dirs0, (entries3 -- str)[str0, entries3[str]][name] ∈ files, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Rule argument

Additional information

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