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Proof step 221 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[m] = mkientry(boolvar1, mkinode(m1, md1, false, 0, m8, m9)), cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), cache_files[m] = mkfile(m0, md0, 0, content), (∅)[ino] = mkientry(boolvar0, mkinode(m2, md, boolvar, m3, m4, m5)), cache_pcache[datakey(ino, n)] = mkpentry(boolvar2, buf), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), datakey(ino, n) ∈ cache_pcache, m ∈ cache_files, ino ∈ cache_files, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ buf = content1[n], m = ROOT_INO, m ∈ cache_dirs, ino ∈ cache_icache, datakey(ino, n) ∈ evict(m, cache_pcache)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: pcache-del-ops name: in-evict-other seq: ⊦ ino ≠ ino0 → ( datakey(ino, pageno) ∈ evict(ino0, pcache) ↔ datakey(ino, pageno) ∈ pcache) subst: [pcache, ino0, pageno, ino] → [cache_pcache, m, n, ino] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s) Used terms: cache_pcache, m, n, ino