[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 179 from proof refine-evict (previous step)

# 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[n], m = ROOT_INO, m ∈ cache_dirs, ino ∈ cache_icache, datakey(ino, n) ∈ evict(m, cache_pcache)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 180:
⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1
Proof step 181:
# links(m, cache_dirs) = 0, cache_pcache[datakey(ino, n)] = mkpentry(boolvar1, buf), 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), 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?, n ∈ content1 ∨ n ∈ mkcontent(ino, cache_pcache) ⊦ buf = content1[n], m = ROOT_INO, datakey(ino, n) ∈ evict(m, cache_pcache), ino ∈ cache_icache, m ∈ cache_dirs

Rule argument

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

Additional information

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