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Proof step 475 from proof inv-rename-file-dentry (previous step)

(key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]) = mkfile(m2, md, m5, content0), pcache[key] = mkpentry(boolvar, buf), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), key ∈ pcache, m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf = content0[key.part])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 476:
⊦ 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 477:
(key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]) = mkfile(m2, md, m5, content0), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), pcache[key] = mkpentry(boolvar, buf), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, key ∈ pcache, asynced2 → synced(files, icache0, pcache), ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs0, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf = content0[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, files] flags: <all paths>

Additional information

Used terms: pcache, dirs0, files