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Proof step 864 from proof refine-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), 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), m2 / VFS_PAGE_SIZE ∈ content, m1 ∈ cache_files, key ∈ cache_pcache, m2 ≤ m, 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]) ⊦ m2 % VFS_PAGE_SIZE = 0, key.data?, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 865:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), 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), key ∈ cache_pcache, m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key0. key0 ∈ cache_pcache → key0.data? ∧ # cache_pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ cache_files ∧ (¬ cache_pcache[key0].dirty → key0.part ∈ cache_files[key0.ino].content ∧ cache_pcache[key0].page = cache_files[key0.ino].content[key0.part]) ⊦ m2 % VFS_PAGE_SIZE = 0, key.data?, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Rule argument

Additional information

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