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Proof step 239 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), cache_files[m] = mkfile(m0, md0, 0, content), cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), 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, m ∈ cache_dirs, (n ∈ content1 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache))) ∧ ( n ∈ content1 ⊕ mkcontent(ino, cache_pcache) → (content1 ⊕ mkcontent(ino, cache_pcache))[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 240:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 241:
# links(m, cache_dirs) = 0, cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), cache_files[m] = mkfile(m0, md0, 0, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), 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, m ∈ cache_dirs, (n ∈ content1 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache))) ∧ ( n ∈ content1 ⊕ mkcontent(ino, cache_pcache) → (content1 ⊕ mkcontent(ino, cache_pcache))[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n]), m ∈ cache_icache ∧ ¬ cache_icache[m].inode.directory
Proof step 298:
# links(m, cache_dirs) = 0, cache_files[ino] = mkfile(m6, md2, # links(ino, cache_dirs), content1), cache_files[m] = mkfile(m0, md0, 0, content), cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, true, m3, m4, m5)), mkfile(cache_icache[m].inode.size, cache_icache[m].inode.meta, cache_icache[m].inode.nlink, (cache_files ⊕ cache_pcache)[m].content) = 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, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ino = m, m = ROOT_INO, cache_icache[m].inode.directory, m ∈ cache_dirs, (n ∈ content1 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content1 ⊕ mkcontent(ino, evict(m, cache_pcache))) ∧ ( n ∈ content1 ⊕ mkcontent(ino, cache_pcache) → (content1 ⊕ mkcontent(ino, cache_pcache))[n] = (content1 ⊕ mkcontent(ino, evict(m, cache_pcache)))[n])

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [m, cache_icache, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used terms: m, cache_icache, cache_files ⊕ cache_pcache