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Proof step 44 from proof inv-lookup (previous step)

dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), dirs[key.ino] = mkdir(m0, md0, m2, m3, entries0), afs-cons(dirs, files), synced(dirs, icache, pcache), dent0.name ∈ entries, p_ino ∈ dirs, key ∈ dcache, asynced1 → synced(files, icache, pcache), ∀ 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?, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ dentrykey(p_ino, dent0.name) ∈ dcache, 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 ∈ entries0 ∧ dcache[key].ino = entries0[dcache[key].name] ∧ dcache[key].dentry?

Heuristic use patterns applied rule all left

And closed the goal!

Rule argument

pos: left 9 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