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Proof step 355 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ pcache-cons(truncate(m0, min(m5, m2), pcache0), dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 356:
⊦ 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 357:
# buf0 = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ∀ key. key ∈ truncate(m0, min(m5, m2), pcache0) → key.data? ∧ # truncate(m0, min(m5, m2), pcache0)[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ ( ¬ truncate(m0, min(m5, m2), pcache0)[key].dirty → key.part ∈ files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))][key.ino].content ∧ truncate(m0, min(m5, m2), pcache0)[key].page = files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))][key.ino].content[key.part]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

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] → [truncate(m0, min(m5, m2), pcache0), dirs, files0 [m0, mkfile (m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ]] flags: <all paths>

Additional information

Used terms: truncate(m0, min(m5, m2), pcache0), dirs, files0 [m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ]