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Proof step 1 from proof refine-lookup (conclusion)

pre-lookup(p_ino, dent, afs_dirs, afs_files), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs_asynced ↔ cache_asynced, afs-cons(afs_dirs, afs_files), icache-cons(cache_icache, cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), afs-cons(cache_dirs, cache_files), dent = dent0, err = err0 ⊦ ⟪cache_lookup#(p_ino, cache_dirs, cache_files, cache_asynced; dent, err, cache_dcache)⟫ ⟨afs_lookup#(p_ino, afs_dirs, afs_files, afs_asynced; dent0, err0)⟩ ((afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)) ∧ dent = dent0 ∧ err = err0)

System applied rule normalize

And obtained the following new goals

Rule argument

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