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Proof step 381 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_files[m] = mkfile(m0, md0, 0, content), cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), cache_icache[m] = mkientry(boolvar1, mkinode(m7, md3, true, m8, m9, m10)), cache_icache[ino] = mkientry(boolvar, mkinode(m2, md, false, m3, m4, m5)), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), 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), m ∈ cache_icache, ino ∈ cache_icache, ino ∈ cache_files, m ∈ cache_files, n ∈ content1 ⊕ mkcontent(ino, cache_pcache), n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache)), cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ (content1 ⊕ mkcontent(ino, cache_pcache))[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n], ino = m, m = ROOT_INO, m ∈ cache_dirs, n ∈ mkcontent(ino, cache_pcache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 382:
# links(m, cache_dirs) = 0, cache_icache[ino] = mkientry(boolvar, mkinode(m2, md, false, m3, m4, m5)), cache_icache[m] = mkientry(boolvar1, mkinode(m7, md3, true, m8, m9, m10)), cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), cache_files[m] = mkfile(m0, md0, 0, content), 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), m ∈ cache_files, ino ∈ cache_files, ino ∈ cache_icache, m ∈ cache_icache, n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache)), n ∈ content1, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ content1[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n], ino = m, m = ROOT_INO, m ∈ cache_dirs, datakey(ino, n) ∈ cache_pcache

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)