[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 32 from proof refine-lookup (previous step)

cache_dirs[p_ino] = mkdir(m, md, # links(p_ino, cache_dirs), m1, entries), cache_dcache[dentrykey(p_ino, dent0.name)] ≠ mkdentry(dent0.name, entries[dent0.name]), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(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), dent0.name ∈ entries, dentrykey(p_ino, dent0.name) ∈ cache_dcache, p_ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_dcache → key.dentry? ∧ key.name = cache_dcache[key].name ∧ key.ino ∈ cache_dirs ∧ (links(key.ino, cache_dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (cache_dcache[key].ino ∈ cache_dirs ∨ cache_dcache[key].ino ∈ cache_files) ∧ cache_dcache[key].name ∈ cache_dirs[key.ino].entries ∧ cache_dcache[key].ino = cache_dirs[key.ino].entries[cache_dcache[key].name] ∧ cache_dcache[key].dentry?, links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (cache_dcache[dentrykey(p_ino, dent0.name)] = dent0 ∧ ESUCCESS = err)

User applied rule all left

And obtained the following new goals

Proof step 33:
cache_dirs[p_ino] = mkdir(m, md, # links(p_ino, cache_dirs), m1, entries), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), p_ino ∈ cache_dirs, dentrykey(p_ino, dent0.name) ∈ cache_dcache, dent0.name ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), dentrykey(p_ino, dent0.name) ∈ cache_dcache → dentrykey(p_ino, dent0.name).dentry? ∧ dentrykey(p_ino, dent0.name).name = cache_dcache[dentrykey(p_ino, dent0.name)].name ∧ dentrykey(p_ino, dent0.name).ino ∈ cache_dirs ∧ (links(dentrykey(p_ino, dent0.name).ino, cache_dirs) ≠ ∅ ∨ dentrykey(p_ino, dent0.name).ino = ROOT_INO) ∧ (cache_dcache[dentrykey(p_ino, dent0.name)].ino ∈ cache_dirs ∨ cache_dcache[dentrykey(p_ino, dent0.name)].ino ∈ cache_files) ∧ cache_dcache[dentrykey(p_ino, dent0.name)].name ∈ cache_dirs[dentrykey(p_ino, dent0.name).ino].entries ∧ cache_dcache[dentrykey(p_ino, dent0.name)].ino = cache_dirs[dentrykey(p_ino, dent0.name).ino].entries[cache_dcache[dentrykey(p_ino, dent0.name)].name] ∧ cache_dcache[dentrykey(p_ino, dent0.name)].dentry?, ∀ key. key ∈ cache_dcache → key.dentry? ∧ key.name = cache_dcache[key].name ∧ key.ino ∈ cache_dirs ∧ (links(key.ino, cache_dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (cache_dcache[key].ino ∈ cache_dirs ∨ cache_dcache[key].ino ∈ cache_files) ∧ cache_dcache[key].name ∈ cache_dirs[key.ino].entries ∧ cache_dcache[key].ino = cache_dirs[key.ino].entries[cache_dcache[key].name] ∧ cache_dcache[key].dentry?, links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (cache_dcache[dentrykey(p_ino, dent0.name)] = dent0 ∧ ESUCCESS = err), cache_dcache[dentrykey(p_ino, dent0.name)] = mkdentry(dent0.name, entries[dent0.name])

Rule argument

pos: left 12 terms: dentrykey(p_ino, dent0.name) abort: F discard: F computed: T

Additional information

Used terms: dentrykey(p_ino, dent0.name)