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Proof step 328 from proof refine-rmdir (previous step)

# links(entries0[str], cache_dirs) = m1, # links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m].nsubdirs = 0, entries0[str] = cache_dirs[m].entries[str], cache_dirs[entries0[str]] = mkdir(m0, md3, m1, m2, ∅), cache_dirs[m] = mkdir(cache_dirs[m].size, md1, cache_dirs[m].nlink, 0, entries0), cache_dirs[entries0[str]] = mkdir(m0, md, m1, m2, entries), 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), str ∈ cache_dirs[m].entries, str ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_dirs, 1 ≤ cache_dirs[m].size, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), cache_dirs[m].size = 0, entries0[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 329:
# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m].nsubdirs = 0, cache_dirs[m] = mkdir(cache_dirs[m].size, md1, cache_dirs[m].nlink, 0, entries0), cache_dirs[entries0[str]] = mkdir(m0, md, # links(entries0[str], cache_dirs), m2, ∅), entries0[str] = cache_dirs[m].entries[str], cache_dirs[m].size ≠ 0, entries0[str] ≠ ROOT_INO, 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), entries0[str] ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries0, str ∈ cache_dirs[m].entries, 1 ≤ cache_dirs[m].size, ⌊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)