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Proof step 135 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[m].inode = mkinode(m7, md3, boolvar1, m8, m9, m10), (∅)[ino] = mkientry(boolvar0, mkinode(m2, md, boolvar, 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, # 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_files, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ino = m, m = ROOT_INO, ino ∈ cache_icache, m ∈ cache_dirs, m ∈ cache_icache ∧ ¬ boolvar1, (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 elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 136:
# links(m, cache_dirs) = 0, cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), cache_files[m] = mkfile(m0, md0, 0, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), (∅)[ino] = mkientry(boolvar0, mkinode(m2, md, boolvar, m3, m4, m5)), cache_icache[m] = mkientry(boolvar2, inode), inode = mkinode(m7, md3, boolvar1, m8, m9, m10), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ino = m, m = ROOT_INO, m ∈ cache_dirs, ino ∈ 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]), m ∈ cache_icache ∧ ¬ boolvar1

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [cache_icache[m], boolvar2, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: cache_icache[m], boolvar2, inode