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Proof step 225 from proof inv-rename-file-negdentry (previous step)

# links (entries[str], dirs0[m8, mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)] [m, mkdir(m1 + 1, md5, # links(m, dirs0), m14, entries1[str0, entries[str]]) ]) = # links(entries[str], dirs0), (m19 = m ⊃ mkdir(m1 + 1, md5, # links(m, dirs0), m14, entries1[str0, entries[str]]);mkdir(m18, md8, # links(m19, dirs0), m20, entries5)) = mkdir(m15, md7, 0, m17, entries4), dcache0[dentrykey(m19, str1)] = mkdentry(str1, entries5[str1]), dirs0[m] = mkdir(m1, md4, # links(m, dirs0), m14, entries1), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), dirs0[m19] = mkdir(m18, md8, # links(m19, dirs0), m20, entries5), afs-cons (dirs0[m8, mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)] [m, mkdir(m1 + 1, md5, # links(m, dirs0), m14, entries1[str0, entries[str]]) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), str1 ∈ entries5, m19 ∈ dirs0, dentrykey(m19, str1) ∈ dcache0, m ∈ dirs0, m8 ∈ dirs0, entries[str] ∈ files, str ∈ entries, asynced2 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry?, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files ⊦ # links(m, dirs0) = 0, # links(m19, dirs0) = 0, dentrykey(m19, str1) = dentrykey(m8, str), dentrykey(m19, str1) = dentrykey(m, str0), links(m, dirs0) = ∅, links(m19, dirs0) = ∅, m = ROOT_INO, m = m8, m19 = m8, m19 = ROOT_INO, str0 ∈ entries1, entries[str] ∈ dirs0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 226:
# links (entries[str], dirs0[m8, mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)] [m, mkdir(m1 + 1, md5, # links(m, dirs0), m14, entries1[str0, entries[str]]) ]) = # links(entries[str], dirs0), (m19 = m ⊃ mkdir(m1 + 1, md5, # links(m, dirs0), m14, entries1[str0, entries[str]]);mkdir(m18, md8, # links(m19, dirs0), m20, entries5)) = mkdir(m15, md7, 0, m17, entries4), dirs0[m19] = mkdir(m18, md8, # links(m19, dirs0), m20, entries5), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m1, md4, # links(m, dirs0), m14, entries1), dcache0[dentrykey(m19, str1)] = mkdentry(str1, entries5[str1]), afs-cons(dirs0, files), afs-cons (dirs0[m8, mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)] [m, mkdir(m1 + 1, md5, # links(m, dirs0), m14, entries1[str0, entries[str]]) ], files), synced(dirs0, icache0, pcache), str ∈ entries, entries[str] ∈ files, m8 ∈ dirs0, m ∈ dirs0, dentrykey(m19, str1) ∈ dcache0, m19 ∈ dirs0, str1 ∈ entries5, m ∈ dirs0[m8, mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)], asynced2 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry?, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO ⊦ # links(m19, dirs0) = 0, # links(m, dirs0) = 0, dentrykey(m19, str1) = dentrykey(m, str0), dentrykey(m19, str1) = dentrykey(m8, str), links(m19, dirs0) = ∅, links(m, dirs0) = ∅, m = m8, m = ROOT_INO, m19 = ROOT_INO, m19 = m8, entries[str] ∈ dirs0, str0 ∈ entries1

Rule argument

fma: m ∈ dirs0 [m8, mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str) ]

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s) Used formulas: m ∈ dirs0[m8, mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)]