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Proof step 369 from proof inv-write_inode (previous step)

afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ pcache-cons(pcache, dirs, files[m, (files[m].meta:= md).size:= m2]), m ∈ icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 370:
⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]))
Proof step 371:
afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ m ∈ icache, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files[m, (files[m].meta:= md).size:= m2]) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[m, (files[m].meta:= md).size:= m2][key.ino].content ∧ pcache[key].page = files[m, (files[m].meta:= md).size:= m2][key.ino].content[key.part])

Rule argument

spec: cache-base name: pcache-cons seq: ⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])) subst: [pcache, dirs, files] → [pcache, dirs, files[m, (files[m].meta:= md).size:= m2]] flags: <all paths>

Additional information

Used terms: pcache, dirs, files[m, (files[m].meta:= md).size:= m2]