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Proof step 109 from proof refine-lookup (previous step)

cache_dirs[p_ino] = mkdir(m, md, # links(p_ino, cache_dirs), m1, entries), dent = dent0, 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, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ (err0 = err), dent0.name ∈ entries, dentrykey(p_ino, dent0.name) ∈ cache_dcache, dent0 = negdentry(dent.name) ∧ err0 = ENOENT

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 110:
cache_dirs[p_ino] = mkdir(m, md, # links(p_ino, cache_dirs), m1, entries), err0 ≠ ENOENT, 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, ⌊err0⌋ , ¬ dent0.name ∈ entries, ¬ dentrykey(p_ino, dent0.name) ∈ cache_dcache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ (err0 = err)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ⌊ENOENT⌋ ; (s)