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Proof step 92 from proof inv-evict (previous step)

# links(m, dirs) = 0, dirs[key.ino] = mkdir(m1, md0, m3, m4, entries0), dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs -- m, files), afs-cons(dirs, files), synced(dirs, icache, pcache), key ∈ dcache, m ∈ dirs, asynced1 → synced(files, icache, pcache), key ∈ 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 ∈ dirs[key.ino].entries ∧ dcache[key].ino = dirs[key.ino].entries[dcache[key].name] ∧ dcache[key].dentry?, ∀ 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? ⊦ m = ROOT_INO, key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ≠ m ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs -- m) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ≠ m ∧ dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ entries0 ∧ dcache[key].ino = entries0[dcache[key].name] ∧ dcache[key].dentry?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 93:
# links(m, dirs) = 0, dcache[key].ino = entries0[key.name], key.name = dcache[key].name, dirs[key.ino] = mkdir(m1, md0, # links(key.ino, dirs), m4, entries0), dirs[m] = mkdir(m0, md, 0, m2, entries), key.dentry?, dcache[key].dentry?, afs-cons(dirs -- m, files), afs-cons(dirs, files), synced(dirs, icache, pcache), key.ino ∈ dirs, key ∈ dcache, m ∈ dirs, key.name ∈ entries0, 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?, entries0[key.name] ∈ dirs ∨ entries0[key.name] ∈ files, links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO ⊦ m = ROOT_INO, key.ino ≠ m ∧ (links(key.ino, dirs -- m) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (entries0[key.name] ≠ m ∧ entries0[key.name] ∈ dirs ∨ entries0[key.name] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (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