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Proof step 1509 from proof refine-truncate-buff-none-cached (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), cache_pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf), 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, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, m ∈ cache_files, 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]) ⊦ # buf = VFS_PAGE_SIZE

User applied rule all left

And closed the goal!

Rule argument

pos: left 12 terms: datakey(m, m2 / VFS_PAGE_SIZE) abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s) Used terms: datakey(m, m2 / VFS_PAGE_SIZE)