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Proof step 151 from proof afs-cons-rename-file-dentry (previous step)

# links(entries[str], dirs0) = m11 + 1, (ino = entries[str] ⊃ mkfile(m2, md, m11, content1);mkfile(m12, md7, # links(ino, dirs0), content0)) = mkfile(m14, md8, m15, content2), dirs0[ino] = mkdir(m16, md9, m17, m18, entries2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[ino] = mkfile(m12, md7, # links(ino, dirs0), content0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries[str] ∈ files0, m0 ∈ dirs0, str ∈ entries, entries1[str0] ∈ files0, str0 ∈ entries1, m ∈ dirs0, ino ∈ files0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m0 = m, m15 = # links (ino, dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)] [m, mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ]), entries[str] ∈ dirs0, entries1[str0] ∈ dirs0, ino ∈ dirs0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 152:
# links(entries[str], dirs0) = m11 + 1, (ino = entries[str] ⊃ mkfile(m2, md, m11, content1);mkfile(m12, md7, # links(ino, dirs0), content0)) = mkfile(m14, md8, m15, content2), files0[ino] = mkfile(m12, md7, # links(ino, dirs0), content0), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs0[ino] = mkdir(m16, md9, m17, m18, entries2), afs-cons(dirs0, files0), ino ∈ files0, m ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files0, str ∈ entries, m0 ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, m ∈ dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)], links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m0 = m, m15 = # links (ino, dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)] [m, mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ]), ino ∈ dirs0, entries1[str0] ∈ dirs0, entries[str] ∈ dirs0

Rule argument

fma: m ∈ dirs0 [m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0) ]

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s) Used formulas: m ∈ dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)]