[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 326 from proof refine-link (previous step)

cache_icache[entries0[str]] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m6, m8, m10)), cache_files[entries0[str]] = mkfile(m1, md, # links(entries0[str], cache_dirs), content0), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m5, md1, m7, content), cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), 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), entries0[str] ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ m7 = # links(entries0[str], cache_dirs), str0 ∈ entries, entries0[str] ∈ cache_icache ∧ ¬ boolvar

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: entries0[str] ∈ cache_icache

Additional information

Used simplifier rules: ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s) Used formulas: entries0[str] ∈ cache_icache