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Proof step 110 from proof refine-lookup (previous step)

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)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 111:
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, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨choose err0 with ⌊err0⌋ in err := err0⟩ (err0 = err), err0 = ENOENT, dent0.name ∈ entries, dentrykey(p_ino, dent0.name) ∈ cache_dcache

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};