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Proof step 163 from proof refine-create (previous step)

cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), 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), synced(cache_dirs, cache_icache, cache_pcache), datakey(m, n) ∈ cache_pcache, m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ∧ # cache_pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, cache_dirs, cache_files) ∧ (¬ cache_pcache[key].dirty → key.part ∈ cache_files[key.ino].content ∧ cache_pcache[key].page = cache_files[key.ino].content[key.part]), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m = 0, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 164:
cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), 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), synced(cache_dirs, cache_icache, cache_pcache), m1 ∈ cache_dirs, datakey(m, n) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ∧ # cache_pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ cache_files ∧ (¬ cache_pcache[key].dirty → key.part ∈ cache_files[key.ino].content ∧ cache_pcache[key].page = cache_files[key.ino].content[key.part]), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)