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Proof step 216 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), afs-cons(dirs, files -- m), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ m = ROOT_INO, dcache-cons(dcache, dirs, files -- m), m ∈ dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 217:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))
Proof step 218:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files -- m), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ m = ROOT_INO, m ∈ dirs, ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files -- m)

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [dcache, dirs, files -- m] flags: <all paths>

Additional information

Used terms: dcache, dirs, files -- m