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Proof step 164 from proof inv-mkdir (previous step)

(key.ino = m0 ⊃ mkdir(m3 + 1, md2, # links(key.ino, dirs0), m5 + 1, entries0[str, ino0]) ;(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[key.ino] ) = mkdir(m, md0, m1, m2, entries), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), dirs0[key.ino] = mkdir(m4, md3, m6, m7, entries1), afs-cons(dirs0, files), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, key ∈ dcache[dentrykey(m0, str), mkdentry(str, ino0)], key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ entries1 ∧ dcache[key].ino = entries1[dcache[key].name] ∧ dcache[key].dentry?, asynced1 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key.ino = ino0, ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0, key.dentry? ∧ key.name = dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].name ∧ key.ino ∈ dirs0 ∧ ( links (key.ino, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ]) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].ino = ino0 ∨ dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].ino ∈ dirs0 ∨ dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].ino ∈ files) ∧ dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].name ∈ entries ∧ dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].ino = entries[dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].name] ∧ dcache[dentrykey(m0, str), mkdentry(str, ino0)][key].dentry?

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: key = dentrykey(m0, str)

Additional information

Used simplifier rules: ⊦ dentrykey(m, str).ino = m; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ key ∈ dcache[key, dent]; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ dentrykey(m, str).name = str; (s)% ⊦ dcache[key, dent][key] = dent; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ entries[str, ino][str] = ino; (s)% ⊦ str ∈ entries[str, ino]; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%ino ≠ 0, ¬ ino ∈ dirs ⊦ ino0 ∈ dirs ++ ino ↔ ino0 = ino ∨ ino0 ∈ dirs; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set] Used formulas: key = dentrykey(m0, str)