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Proof step 120 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), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 121:
# 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 ∧ boolvar

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ ino ≠ ino0 → (icache -- ino0)[ino] = icache[ino]; (s)% ⊦ ino ∈ icache -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ icache; (s)