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Proof step 101 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), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache, m1 ∈ files ⊦ pcache-cons(pcache, dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 102:
⊦ 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 103:
files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), dirs[m1] = mkdir(m7, md2, m8, m9, entries), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m1 ∈ files, m ∈ icache, m ∈ files ⊦ ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[m1, mkfile(m4, md, # links(m1, dirs), content0)][key.ino].content ∧ pcache[key].page = files[m1, mkfile(m4, md, # links(m1, dirs), content0)][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[m1, mkfile(m4, md, # links(m1, dirs), content0)]] flags: <all paths>

Additional information

Used terms: pcache, dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]