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Proof step 249 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[m] = mkientry(boolvar1, mkinode(m7, md3, boolvar, m8, m9, m10)), cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), (cache_files ⊕ cache_pcache)[m] = mkfile(m1, md1, 0, content0), cache_files[m] = mkfile(m0, md0, 0, content), cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), 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), ino ∈ cache_icache, ino ∈ cache_files, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ino = m, m = ROOT_INO, m ∈ cache_dirs, m ∈ cache_icache, m ∈ cache_icache ∧ boolvar, m ∈ cache_icache ∧ ¬ boolvar, (n ∈ content1 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache))) ∧ ( n ∈ content1 ⊕ mkcontent(ino, cache_pcache) → (content1 ⊕ mkcontent(ino, cache_pcache))[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 250:
# links(m, cache_dirs) = 0, (∅)[m] = mkientry(boolvar1, mkinode(m7, md3, boolvar, m8, m9, m10)), cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), cache_files[m] = mkfile(m0, md0, 0, content), cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), 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), ino ∈ cache_icache, ino ∈ cache_files, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ m = ROOT_INO, m ∈ cache_dirs, m ∈ cache_icache, (n ∈ content1 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache))) ∧ ( n ∈ content1 ⊕ mkcontent(ino, cache_pcache) → (content1 ⊕ mkcontent(ino, cache_pcache))[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n])

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)