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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 311 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), dirs[key.ino] = mkdir(m5, md1, m6, m7, entries), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files, m ∈ icache, key ∈ dcache, ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs ∧ (links(key0.ino, dirs) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs[key0.ino].entries ∧ dcache[key0].ino = dirs[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry? ⊦ key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ entries ∧ dcache[key].ino = entries[dcache[key].name] ∧ dcache[key].dentry?

Heuristic use patterns applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: key abort: T discard: F computed: F

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% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s) Used terms: key