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Proof step 307 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, false, 0, m8, m9)), cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), cache_files[m] = mkfile(m0, md0, 0, content), 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), n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache)), n ∈ content1 ⊕ mkcontent(ino, cache_pcache), m ∈ cache_files, ino ∈ cache_files, ino ∈ cache_icache, m ∈ cache_icache, 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

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 308:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 309:
# links(m, cache_dirs) = 0, 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), cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, false, 0, m8, m9)), 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)
Proof step 312:
# links(m, cache_dirs) = 0, 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), cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, false, 0, m8, m9)), 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)), n ∈ mkcontent(ino, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ mkcontent(ino, cache_pcache)[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n], ino = m, m = ROOT_INO, m ∈ cache_dirs

Rule argument

spec: cache-base name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n, mkcontent(ino, cache_pcache), content1] flags: <all paths>

Additional information

Used terms: n, mkcontent(ino, cache_pcache), content1