[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 550 from proof inv-rename-dir-dentry (previous step)

(key.ino = entries0[str0] ⊃ mkdir(m, md4, # links(entries0[str0], dirs0), m9, ∅) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);mkdir(m13, md6, m14, m15, entries3)) ) = mkdir(m10, md5, m11, m12, entries2), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m, md3, # links(entries0[str0], dirs0), m9, ∅), dirs0[key.ino] = mkdir(m13, md6, m14, m15, entries3), afs-cons(dirs0, files), afs-cons (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, # links(entries0[str0], dirs0), m9, ∅)], files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], key ∈ dcache0 → key.dentry? ∧ key.name = dcache0[key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache0[key].ino ∈ dirs0 ∨ dcache0[key].ino ∈ files) ∧ dcache0[key].name ∈ entries3 ∧ dcache0[key].ino = entries3[dcache0[key].name] ∧ dcache0[key].dentry?, 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(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, entries0[str0] = m7, key.dentry? ∧ key.name = dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∈ entries2 ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino = entries2[dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name] ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].dentry?

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 551:
(key.ino = entries0[str0] ⊃ mkdir(m, md4, # links(entries0[str0], dirs0), m9, ∅) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);mkdir(m13, md6, m14, m15, entries3)) ) = mkdir(m10, md5, m11, m12, entries2), dirs0[key.ino] = mkdir(m13, md6, m14, m15, entries3), dirs0[entries0[str0]] = mkdir(m, md3, # links(entries0[str0], dirs0), m9, ∅), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), afs-cons (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, # links(entries0[str0], dirs0), m9, ∅)], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], m7 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), key ∈ dcache0 → key.dentry? ∧ key.name = dcache0[key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache0[key].ino ∈ dirs0 ∨ dcache0[key].ino ∈ files) ∧ dcache0[key].name ∈ entries3 ∧ dcache0[key].ino = entries3[dcache0[key].name] ∧ dcache0[key].dentry?, ∀ 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(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = m7, entries0[str0] = ROOT_INO, key = dentrykey(m7, str0), key.dentry? ∧ key.name = dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∈ entries2 ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino = entries2[dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name] ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].dentry?

Rule argument

fma: key = dentrykey(m7, str0)

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 Used formulas: key = dentrykey(m7, str0)