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Proof step 180 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files -- m), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ m = ROOT_INO, synced(dirs, icache -- m, evict(m, pcache)), m ∈ dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 181:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 182:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), afs-cons(dirs, files -- m), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ m = ROOT_INO, m ∈ dirs, ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs → synced(ino, icache -- m, evict(m, pcache))

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 -- m, evict(m, pcache)] flags: <all paths>

Additional information

Used terms: dirs, icache, pcache, dirs, icache -- m, evict(m, pcache)