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Proof step 209 from proof refine-create (previous step)

cache_dirs[m] = mkdir(m0, md, # links(m, cache_dirs), m2, 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), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str ∈ entries, ∃ ino. ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ cache_files ∧ ino ≠ 0

User applied rule apply lemma

And obtained the following new goals

Proof step 210:
⊦ ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files
Proof step 211:
cache_dirs[m] = mkdir(m0, md, # links(m, cache_dirs), m2, entries), 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_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ cache_files, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str ∈ entries, ∃ ino. ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ cache_files ∧ ino ≠ 0

Rule argument

spec: afs-base name: new-exists seq: ⊦ ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files subst: [dirs, files] → [cache_dirs, cache_files]

Additional information

Used terms: cache_dirs, cache_files