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Proof step 254 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, files1[m] = mkfile(m3, md, # links(m, dirs), content1), files0[m] = mkfile(m1, md0, # links(m, dirs), content), pcache[datakey(m, n0)] = mkpentry(true, buf), n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files1), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, ⌊err0⌋ ⊦ icache-cons(icache, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 255:
⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) ))
Proof step 256:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files1[m] = mkfile(m3, md, # links(m, dirs), content1), n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), icache-cons(icache, dirs, files1), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, ⌊err0⌋ ⊦ ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]) ; valid-ino(ino, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]) ∧ valid-inode(icache[ino].inode, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]) )

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ; valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) )) subst: [icache, dirs, files] → [icache, dirs, files1 [m, mkfile(m3, md, # links(m, dirs), content1[n0, buf]) ]] flags: <all paths>

Additional information

Used terms: icache, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]