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Proof step 31 from proof refine-lookup (previous step)

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), ∀ key. key ∈ cache_dcache → key.dentry? ∧ key.name = cache_dcache[key].name ∧ valid-dentry(key.ino, cache_dcache[key], cache_dirs, cache_files), 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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
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)

Rule argument

Additional information

Used simplifier rules: ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)