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Proof step 317 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_files[m] = mkfile(m0, md0, 0, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, 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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, ino ∈ cache_files, ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ino = m, m = ROOT_INO, mkfile (cache_icache[ino].inode.size, cache_icache[ino].inode.meta, cache_icache[ino].inode.nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)) = mkfile (cache_icache[ino].inode.size, cache_icache[ino].inode.meta, cache_icache[ino].inode.nlink, cache_files[ino].content ⊕ mkcontent(ino, evict(m, cache_pcache))), cache_icache[ino].inode.directory, m ∈ cache_dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 318:
# links(m, cache_dirs) = 0, cache_icache[ino].inode = mkinode(m2, md, boolvar, m3, m4, m5), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), cache_files[m] = mkfile(m0, md0, 0, content), ¬ boolvar, 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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_icache, ino ∈ cache_files, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ino = m, m = ROOT_INO, mkfile(m5, md, m3, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)) = mkfile(m5, md, m3, cache_files[ino].content ⊕ mkcontent(ino, evict(m, cache_pcache))), m ∈ cache_dirs

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[ino].inode, m2, md, boolvar, m3, m4, m5]

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[ino].inode, m2, md, boolvar, m3, m4, m5