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Proof step 165 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[key.ino] = mkdir(m4, md3, m6, m7, entries1), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), 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), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), key ∈ dcache[dentrykey(m0, str), mkdentry(str, ino0)], m0 ∈ dirs0, asynced1 → synced(files, icache0, pcache), 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?, ∀ 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, key = dentrykey(m0, str), str ∈ entries0, ino0 ∈ files, ino0 ∈ dirs0, 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 166:
dcache[key].ino = entries1[key.name], key.name = dcache[key].name, (key.ino = m0 ⊃ mkdir(m3 + 1, md2, # links(key.ino, dirs0), m5 + 1, entries0[str, ino0]) ;mkdir(m4, md3, # links(key.ino, dirs0), m7, entries1) ) = mkdir(m, md0, m1, m2, entries), dirs0[key.ino] = mkdir(m4, md3, # links(key.ino, dirs0), m7, entries1), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), dcache[key].dentry?, key.dentry?, 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), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), key.name ∈ entries1, key.ino ∈ dirs0, key ∈ dcache, m0 ∈ dirs0, 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?, entries1[key.name] ∈ dirs0 ∨ entries1[key.name] ∈ files, links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino0 = 0, key = dentrykey(m0, str), str ∈ entries0, ino0 ∈ files, ino0 ∈ 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) ∧ (entries1[key.name] = ino0 ∨ entries1[key.name] ∈ dirs0 ∨ entries1[key.name] ∈ files) ∧ key.name ∈ entries ∧ entries1[key.name] = entries[key.name]

Rule argument

Additional information

Used simplifier rules: 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% ⊦ key ≠ key0 → dcache[key0, dent][key] = dcache[key]; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%ino ∈ dirs, ino0 ≠ 0, ¬ ino0 ∈ dirs ⊦ ino ≠ ino0 → (dirs ++ ino0)[ino] = dirs[ino]; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ key ≠ key0 → (key ∈ dcache[key0, dent] ↔ key ∈ dcache); (s)