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Proof step 392 from proof inv-write_inode (previous step)

dirs[key.ino] = mkdir(m0, md0, m1, m3, entries), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), dcache-cons(dcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files, key ∈ dcache ⊦ m ∈ icache, 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 insert rewrite lemma

And obtained the following new goals

Proof step 393:
⊦ 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 394:
dirs[key.ino] = mkdir(m0, md0, m1, m3, entries), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), key ∈ dcache, m ∈ files, ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files) ⊦ m ∈ icache, 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?

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] flags: <all paths>

Additional information

Used terms: dcache, dirs, files