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Proof step 294 from proof inv-truncate-buff-none-uncached (previous step)

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

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 295:
⊦ synced(files, icache, pcache) → (¬ synced(files0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0)))
Proof step 296:
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))]), synced(files0, icache, pcache0), m0 ∈ files0, ∀ key. key ∈ pcache0 → key.data? ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, ∀ ino. (ino ∈ files0 → synced(ino, icache, pcache0)) → ino ∈ files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))] → synced(ino, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0)), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Rule argument

spec: cache-base name: synced-files-variant1 seq: ⊦ synced(files, icache, pcache) → ( ¬ synced(files0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0))) subst: [files, icache, pcache, files0, icache0, pcache0] → [files0, icache, pcache0, files0 [m0, mkfile (m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ], icache [m0, mkientry (false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ], truncate(m0, min(m5, m2), pcache0)] flags: <all paths>

Additional information

Used terms: files0, icache, pcache0, files0 [m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ], icache [m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ], truncate(m0, min(m5, m2), pcache0)