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Proof step 47 from proof fsync-pages-inv (previous step)

files[m] = mkfile(m0, md1, # links(m, dirs), content0), files0[m] = mkfile(m1, md0, # links(m, dirs), content), pcache[datakey(m, n0)] = mkpentry(true, buf), n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files, datakey(m, n0) ∈ pcache ⊦ # buf = VFS_PAGE_SIZE

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ 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 49:
pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files[m] = mkfile(m0, md1, # links(m, dirs), content0), n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files), icache-cons(icache, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), datakey(m, n0) ∈ pcache, m ∈ files, m ∈ files0, ∀ 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]) ⊦ # buf = VFS_PAGE_SIZE

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: [files, dirs, pcache] → [files, dirs, pcache] flags: <all paths>

Additional information

Used terms: files, dirs, pcache