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Proof step 231 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_files[m] = mkfile(m0, md0, 0, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ino = m, m = ROOT_INO, mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)) = mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, evict(m, cache_pcache))), m ∈ cache_dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 232:
# links(m, cache_dirs) = 0, cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), cache_files[m] = mkfile(m0, md0, 0, content), cache_files[ino] = mkfile(m6, md2, m7, 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, mkfile(m6, md2, m7, content1 ⊕ mkcontent(ino, cache_pcache)) = mkfile(m6, md2, m7, content1 ⊕ mkcontent(ino, evict(m, cache_pcache))), m ∈ cache_dirs

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [cache_files[ino], m6, md2, m7, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: cache_files[ino], m6, md2, m7, content1