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Proof step 175 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(boolvar2, mkinode(m7, md3, true, m8, m9, m10)), (∅)[ino] = mkientry(boolvar0, mkinode(m2, md, boolvar, 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), n ∈ content1 ⊕ mkcontent(ino, cache_pcache), m ∈ cache_icache, ino ∈ cache_files, m ∈ cache_files, datakey(ino, n) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ cache_pcache[datakey(ino, n)].page = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n], m = ROOT_INO, ino ∈ cache_icache, m ∈ cache_dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 176:
# links(m, cache_dirs) = 0, (∅)[ino] = mkientry(boolvar0, mkinode(m2, md, boolvar, m3, m4, m5)), cache_icache[m] = mkientry(boolvar2, 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), cache_pcache[datakey(ino, n)] = mkpentry(boolvar1, 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, n ∈ content1 ⊕ mkcontent(ino, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ buf = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n], m = ROOT_INO, m ∈ cache_dirs, ino ∈ cache_icache

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [cache_pcache[datakey(ino, n)], boolvar1, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: cache_pcache[datakey(ino, n)], boolvar1, buf