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Proof step 143 from proof afs-cons-rename-file-negdentry (previous step)

# entries1 = m1 + 1, files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(m1 + 1, md2, # links(m, dirs0), # subdirs(m, dirs0), entries1), files[m] = mkfile(m8, md3, m10, content), afs-cons(dirs0, files), m ∈ dirs0, entries1[str] ∈ files, str ∈ entries1, ROOT_INO ∈ dirs0, name ∈ (entries1 -- str)[str0, entries1[str]], # links(m, dirs0) ≤ 1, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1 = ∅, name = str0, (entries1 -- str)[str0, entries1[str]][name] ∈ files, (entries1 -- str)[str0, entries1[str]][name] ∈ dirs0, str0 ∈ entries1, entries1[str] ∈ dirs0, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 144:
# entries1 = m1 + 1, files[m] = mkfile(m8, md3, m10, content), dirs0[m] = mkdir(m1 + 1, md2, # links(m, dirs0), # subdirs(m, dirs0), entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m ∈ dirs0, name ∈ entries1, # links(m, dirs0) ≤ 1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files ⊦ entries1 = ∅, name = str, entries1[str] ∈ dirs0, str0 ∈ entries1, (entries1 -- str)[str0, entries1[str]][name] ∈ dirs0, (entries1 -- str)[str0, entries1[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)