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Proof step 1 from proof refine-write_inode (conclusion)

pre-write-inode(inode, 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), err = err0 ⊦ ⟪cache_write_inode#(inode, cache_sync; err, cache_dirs, cache_files, cache_icache, cache_asynced)⟫ ⟨afs_write_inode#(inode; err0, afs_dirs, afs_files; afs_asynced)⟩ ((afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)) ∧ err = err0)

System applied rule normalize

And obtained the following new goals

Rule argument

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