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Proof step 84 from proof refine-lookup (previous step)

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, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪fail#(; ; err); dent := dent0; if err = ESUCCESS then dcache_set#(p_ino, dent0.name, dent; err, cache_dcache)⟫ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (dent = dent0 ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 85:
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 ⊦ ⟪choose err0 with ⌊err0⌋ in err := err0; dent := dent0; if err = ESUCCESS then dcache_set#(p_ino, dent0.name, dent; err, cache_dcache)⟫ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (dent = dent0 ∧ err = err0), 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};