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Proof step 2 from proof refine-readdir (previous step)

afs_asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, strings = strings0, afs-cons(cache_dirs, cache_files), afs-cons(afs_dirs, afs_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), pre-readdir(inode.ino, afs_dirs, afs_files), synced(cache_dirs, cache_icache, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_readdir#(inode, cache_dirs, cache_files, cache_asynced; strings, err)⟫ ⟨afs_readdir#(inode, afs_dirs, afs_files, afs_asynced; strings0, err0)⟩ ( (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)) ∧ strings = strings0 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ pre-readdir(ino, dirs, files) ↔ valid-dir-ino(ino, dirs, files); (s)