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Proof step 426 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, (cache_files ⊕ cache_pcache)[m] = mkfile(m1, md1, 0, content0), cache_files[m] = mkfile(m0, md0, 0, content), cache_icache[m] = mkientry(boolvar0, mkinode(m2, md, boolvar, m3, m4, m5)), cache_icache[m].inode.directory, 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), m ∈ cache_files, key ∈ cache_pcache, m ∈ cache_icache, 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]) ⊦ m = ROOT_INO, key.data?, m ∈ cache_dirs, m ∈ cache_icache ∧ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 427:
# links(m, cache_dirs) = 0, cache_files[m] = mkfile(m0, md0, 0, content), cache_icache[m] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), 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), m ∈ cache_files, key ∈ cache_pcache, m ∈ cache_icache, 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]) ⊦ m = ROOT_INO, key.data?, m ∈ cache_dirs

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (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)