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Proof step 127 from proof fsync-inode-inv (previous step)

icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), dirs[m1] = mkdir(m7, md2, m8, m9, entries), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), dirs[key.ino] = mkdir(m2, md3, m3, m6, entries0), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache, m1 ∈ files, 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 ∈ 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 13 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