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Proof step 869 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, 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) ⊕ cache_icache)[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), m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, key ∈ cache_pcache, 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?, m3 ∈ cache_icache ∧ ¬ cache_icache[m3].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 870:
# buf0 = VFS_PAGE_SIZE, cache_icache[m3].inode = mkinode(m4, md, boolvar0, m5, m6, m7), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_pcache[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), 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, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, m3 ∈ cache_files, 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?, m3 ∈ cache_icache ∧ ¬ boolvar0

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [cache_icache[m3].inode, m4, md, boolvar0, m5, m6, m7]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: cache_icache[m3].inode, m4, md, boolvar0, m5, m6, m7