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Proof step 342 from proof refine-rmdir (previous step)

# links(entries[str], cache_dirs) = m1, cache_dirs[m] = mkdir(0, md, # links(m, cache_dirs), m2, entries), cache_dirs[entries[str]] = mkdir(m0, md3, m1, m3, ∅), cache_dirs[entries[str]] = mkdir(m0, md0, m1, m3, entries0), entries0 = ∅, 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), entries[str] ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 343:
cache_dirs[entries[str]] = mkdir(m0, md0, # links(entries[str], cache_dirs), m3, ∅), cache_dirs[m] = mkdir(0, md, # links(m, cache_dirs), m2, entries), entries[str] ≠ ROOT_INO, 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), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_dirs, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err)

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)