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Proof step 158 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files ⊦ synced(dirs, icache, pcache[datakey(m, pageno), mkpentry(true, buf)])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 159:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 160:
# buf = VFS_PAGE_SIZE, afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files ⊦ ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs → synced(ino, icache, pcache[datakey(m, pageno), mkpentry(true, buf)])

Rule argument

spec: cache-base name: synced-dirs-variant1 seq: ⊦ synced(dirs, icache, pcache) → ( ¬ synced(dirs0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0))) subst: [dirs, icache, pcache, dirs0, icache0, pcache0] → [dirs, icache, pcache, dirs, icache, pcache[datakey(m, pageno), mkpentry(true, buf)]] flags: <all paths>

Additional information

Used terms: dirs, icache, pcache, dirs, icache, pcache[datakey(m, pageno), mkpentry(true, buf)]