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Proof step 323 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[ino] = mkientry(boolvar, mkinode(m2, md, false, 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, mkfile(m5, md, m3, content1 ⊕ mkcontent(ino, cache_pcache)) = mkfile(m5, md, m3, content1 ⊕ mkcontent(ino, evict(m, cache_pcache))), m ∈ cache_dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 324:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 325:
# 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(boolvar, mkinode(m2, md, false, 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, m5 = m5 ∧ md = md ∧ m3 = m3 ∧ content1 ⊕ mkcontent(ino, cache_pcache) = content1 ⊕ mkcontent(ino, evict(m, cache_pcache))

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [m, md, m0, content, m1, md0, m2, content0] → [m5, md, m3, content1 ⊕ mkcontent(ino, cache_pcache), m5, md, m3, content1 ⊕ mkcontent(ino, evict(m, cache_pcache))] flags: <all paths>

Additional information

Used terms: m5, md, m3, content1 ⊕ mkcontent(ino, cache_pcache), m5, md, m3, content1 ⊕ mkcontent(ino, evict(m, cache_pcache))