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Proof step 72 from proof refine-lookup (previous step)

asynced ↔ cache_asynced, dent = negdentry(dent1.name), dent1 = dent0, dirs = cache_dirs, err = ENOENT, err1 = ESUCCESS, files = cache_files, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪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, dent1.name ∈ dirs[p_ino].entries

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 73:
asynced ↔ cache_asynced, dent = negdentry(dent1.name), dent1 = dent0, dirs = cache_dirs, err = ENOENT, err1 = ESUCCESS, files = cache_files, 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 ⊦ ⟪skip⟫ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (dent = dent0 ∧ err = err0), dent1.name ∈ dirs[p_ino].entries, dentrykey(p_ino, dent0.name) ∈ cache_dcache

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ESUCCESS ≠ ENOENT; (s)