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Proof step 118 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[ino] = mkientry(boolvar0, 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), 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_files, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = (((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m))[ino], ino = m, m = ROOT_INO, m ∈ cache_dirs, ino ∈ cache_icache ∧ ¬ boolvar

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 120:
# 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), cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, boolvar, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = (((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m))[ino], ino = m, m = ROOT_INO, m ∈ cache_dirs, ino ∈ cache_icache ∧ ¬ boolvar, ino ∈ cache_icache -- m ∧ (cache_icache -- m)[ino].inode.directory
Proof step 230:
# 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), cache_icache[ino] = mkientry(boolvar0, mkinode(m2, md, boolvar, m3, m4, m5)), (cache_icache -- m)[ino].inode.directory, 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_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files -- m) ⊕ evict(m, cache_pcache))[ino], ino = m, m = ROOT_INO, m ∈ cache_dirs, ino ∈ cache_icache ∧ ¬ boolvar

Rule argument

spec: cache-base name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [ino, cache_icache -- m, (cache_files -- m) ⊕ evict(m, cache_pcache)] flags: <all paths>

Additional information

Used terms: ino, cache_icache -- m, (cache_files -- m) ⊕ evict(m, cache_pcache)