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Proof step 216 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), dirs[key.ino] = mkdir(m0, md0, m4, m5, entries), afs-cons(dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), synced(dirs, icache, pcache0), datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m3 ∈ files0, key ∈ dcache, m2 ≤ m, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, 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 ∈ files0) ∧ 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 217:
⊦ 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 218:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, dirs[key.ino] = mkdir(m0, md0, m4, m5, entries), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), afs-cons(dirs, files0), afs-cons(dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), synced(dirs, icache, pcache0), key ∈ dcache, m3 ∈ files0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files0) ⊦ m2 % VFS_PAGE_SIZE = 0, 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 ∈ files0) ∧ 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, files0] flags: <all paths>

Additional information

Used terms: dcache, dirs, files0