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Proof step 166 from proof afs-cons-rename-file-negdentry (previous step)

# links(m, dirs0) = m3, # links(m0, dirs0) = dirs0[m0].nlink, dirs0[m] = mkdir(0, md4, m3, m4, entries0), files[entries0[str]] = mkfile(m2, md, # links(entries0[str], dirs0), content0), dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), entries0[str] = entries1[str], dirs0[m] = mkdir(m1, md2, m3, m4, entries1), m1 = 0, afs-cons(dirs0, files), str ∈ entries0, m ∈ dirs0, entries0[str] ∈ files, m0 ∈ dirs0, str ∈ entries1, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ str0 ∈ entries, str0 ∈ dirs0[m0].entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 167:
# links(m0, dirs0) = dirs0[m0].nlink, dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), files[entries1[str]] = mkfile(m2, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(0, md2, # links(m, dirs0), m4, entries1), afs-cons(dirs0, files), m0 ∈ dirs0, entries1[str] ∈ files, m ∈ dirs0, str ∈ entries1, m0 = m → md1 = md0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ dirs0[m0].entries, str0 ∈ entries

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)