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Proof step 6 from proof refine-lookup (previous step)

asynced ↔ false, asynced0 ↔ cache_asynced, dcache = cache_dcache, dent = dent0, dirs = cache_dirs, err = err0, files = cache_files, name = dent.name, 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 ⊦ ⟪dcache_get#(p_ino, name, dcache; asynced, dent, err); if ¬ asynced ∨ err ≠ ESUCCESS then {afs_lookup#(p_ino, dirs, files, asynced0; dent, err); if err = ESUCCESS then dcache_set#(p_ino, name, dent; err, dcache)}⟫ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (dent = dent0 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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