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Proof step 1434 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, cache_icache[m3] = mkientry(boolvar1, mkinode(m, md, boolvar0, m4, m5, m7)), cache_pcache[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (cache_files ⊕ cache_pcache)[m3] = mkfile(m0, md0, # links(m3, 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), key ∈ cache_pcache, m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, 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]) ⊦ key.data?, m3 ∈ cache_icache, m3 ∈ cache_icache ∧ boolvar0, m3 ∈ cache_icache ∧ ¬ boolvar0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1435:
# buf0 = VFS_PAGE_SIZE, (∅)[m3] = mkientry(boolvar1, mkinode(m, md, boolvar0, m4, m5, m7)), cache_pcache[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), 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), key ∈ cache_pcache, m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, 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]) ⊦ key.data?, m3 ∈ cache_icache, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)