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Proof step 130 from proof afs-cons-rename-file-negdentry (previous step)

dirs0[ino] = mkdir(m11, md6, m12, m13, entries), files[ino] = mkfile(m8, md3, # links(ino, dirs0), content), dirs0[m0] = mkdir(m1, md5, # links(m0, dirs0), m6, entries0), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, entries1[str] ∈ files, str ∈ entries1, m0 ∈ dirs0, ROOT_INO ∈ dirs0, ino ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # links(ino, dirs0) = # links (ino, dirs0[m, mkdir(m2, md0, # links(m, dirs0), m5, entries1 -- str)] [m0, mkdir(m1 + 1, md1, # links(m0, dirs0), m6, entries0[str0, entries1[str]]) ]), m = m0, str0 ∈ entries0, entries1[str] ∈ dirs0, ino ∈ dirs0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 131:
dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m0] = mkdir(m1, md5, # links(m0, dirs0), m6, entries0), files[ino] = mkfile(m8, md3, # links(ino, dirs0), content), dirs0[ino] = mkdir(m11, md6, m12, m13, entries), afs-cons(dirs0, files), ino ∈ files, ROOT_INO ∈ dirs0, m0 ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m ∈ dirs0, m0 ∈ dirs0[m, mkdir(m2, md0, # links(m, dirs0), m5, entries1 -- str)], links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links(ino, dirs0) = # links (ino, dirs0[m, mkdir(m2, md0, # links(m, dirs0), m5, entries1 -- str)] [m0, mkdir(m1 + 1, md1, # links(m0, dirs0), m6, entries0[str0, entries1[str]]) ]), m = m0, ino ∈ dirs0, entries1[str] ∈ dirs0, str0 ∈ entries0

Rule argument

fma: m0 ∈ dirs0 [m, mkdir(m2, md0, # links(m, dirs0), m5, entries1 -- str) ]

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s) Used formulas: m0 ∈ dirs0[m, mkdir(m2, md0, # links(m, dirs0), m5, entries1 -- str)]