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Proof step 208 from proof refine-create (previous step)

# links(m, cache_dirs) = m1, cache_dirs[m] = mkdir(m0, md2, m1, m2, entries0), cache_dirs[m] = mkdir(m0, md, m1, 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), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str ∈ entries0, str ∈ entries, ∃ ino. ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ cache_files ∧ ino ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 209:
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

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)