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Proof step 148 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, (key.ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[key.ino]) = mkfile(m, md, m4, content), pcache[key] = mkpentry(boolvar, buf), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), key ∈ pcache, str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 149:
⊦ 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 150:
# links(entries0[str], dirs0) = m2 + 1, (key.ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[key.ino]) = mkfile(m, md, m4, content), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), pcache[key] = mkpentry(boolvar, buf), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, key ∈ pcache, asynced1 → synced(files0, icache0, pcache), ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs0, files0) ∧ (¬ pcache[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache[key].page = files0[key.ino].content[key.part]), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar → key.part ∈ content ∧ buf = 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, dirs0, files0] flags: <all paths>

Additional information

Used terms: pcache, dirs0, files0