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Proof step 80 from proof refine-lookup (previous step)

asynced ↔ cache_asynced, cache_dirs[p_ino] = mkdir(m, md, # links(p_ino, cache_dirs), m1, entries), dent = dent0, dent1 = negdentry(dent0.name), dirs = cache_dirs, err = err0, files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, 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), p_ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ (dent1 = dent ∧ ENOENT = err), ⟨if dent.name ∈ dirs[p_ino].entries then {dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ (dent1 = dent ∧ ENOENT = err), dent0.name ∈ entries, dentrykey(p_ino, dent0.name) ∈ cache_dcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
cache_dirs[p_ino] = mkdir(m, md, # links(p_ino, cache_dirs), m1, 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), p_ino ∈ cache_dirs, ¬ dentrykey(p_ino, dent0.name) ∈ cache_dcache, ¬ dent0.name ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨dent := negdentry(dent0.name); err := ENOENT⟩ (negdentry(dent0.name) = dent ∧ ENOENT = err), ⟨fail#(; ; err)⟩ (negdentry(dent0.name) = dent0 ∧ ENOENT = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)