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

# links(entries0[str], dirs0) = m11 + 1, (ino = m0 ⊃ mkdir(m6, md1, # links(m0, dirs0), m8, (entries0 -- str0)[str, entries0[str0]]) ;mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2) ) = mkdir(m19, md10, m20, m21, entries3), files0[entries0[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries0[str0]] = mkfile(m1, md3, # links(entries0[str0], dirs0), content), dirs0[m0] = mkdir(m6 + 1, md6, # links(m0, dirs0), m8, entries0), dirs0[ino] = mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2), files0[ino] = mkfile(m12, md7, m13, content0), afs-cons(dirs0, files0), ino ∈ dirs0, name ∈ entries3, str0 ∈ entries0, entries0[str0] ∈ files0, str ∈ entries0, m0 ∈ dirs0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ mkdentry(str, entries0[str]) = mkdentry(str0, entries0[str0]), entries0[str0] ∈ dirs0, entries0[str] ∈ dirs0, entries3[name] ∈ dirs0, entries3[name] ∈ files0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 167:
# links(entries0[str], dirs0) = m11 + 1, (ino = m0 ⊃ mkdir(m6, md1, # links(m0, dirs0), m8, (entries0 -- str0)[str, entries0[str0]]) ;mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2) ) = mkdir(m19, md10, m20, m21, entries3), files0[ino] = mkfile(m12, md7, m13, content0), dirs0[ino] = mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2), dirs0[m0] = mkdir(m6 + 1, md6, # links(m0, dirs0), m8, entries0), files0[entries0[str0]] = mkfile(m1, md3, # links(entries0[str0], dirs0), content), files0[entries0[str]] = mkfile(m5, md0, m11 + 1, content1), ino = m0, afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries0[str] ∈ files0, m0 ∈ dirs0, str ∈ entries0, entries0[str0] ∈ files0, str0 ∈ entries0, name ∈ entries3, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ mkdentry(str, entries0[str]) = mkdentry(str0, entries0[str0]), entries3[name] ∈ files0, entries3[name] ∈ dirs0, entries0[str] ∈ dirs0, entries0[str0] ∈ dirs0

Rule argument

fma: ino = m0

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)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss) Used formulas: ino = m0