[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 814 from proof refine-rename-file-dentry (previous step)

cache_files[entries1[str0]] = mkfile(m0, md6, # links(entries1[str0], cache_dirs), content3), cache_dirs[m] = mkdir(m2, md2, # links(m, cache_dirs), m6, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str0]] = mkfile(m8, md4, # links(entries1[str0], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m12, md3, # links(entries0[str], cache_dirs), content), cache_dirs[m3] = mkdir(0, md1, # links(m3, cache_dirs), m5, entries1), cache_files[entries0[str]] = mkfile(m1, md5, # links(entries0[str], cache_dirs), content2), 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), str0 ∈ entries1, str ∈ entries0, m ∈ cache_dirs, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, entries1[str0] ∈ cache_files, ⌊err1⌋ , ¬ entries0[str] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), m3 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])

Heuristic use patterns applied rule exists right

And obtained the following new goals

Proof step 815:
cache_files[entries0[str]] = mkfile(m1, md5, # links(entries0[str], cache_dirs), content2), cache_dirs[m3] = mkdir(0, md1, # links(m3, cache_dirs), m5, entries1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m12, md3, # links(entries0[str], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str0]] = mkfile(m8, md4, # links(entries1[str0], cache_dirs), content0), cache_dirs[m] = mkdir(m2, md2, # links(m, cache_dirs), m6, entries0), cache_files[entries1[str0]] = mkfile(m0, md6, # links(entries1[str0], cache_dirs), content3), 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), entries1[str0] ∈ cache_files, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries0, str0 ∈ entries1, ⌊err1⌋ , m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⌊err1⌋ ∧ ⟨err := err1; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), entries0[str] ∈ cache_dirs, m3 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])

Rule argument

pos: right 1 terms: err1 abort: T discard: F computed: F

Additional information

Used terms: err1