[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 109 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache) -- m = ((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m), m = ROOT_INO, m ∈ cache_dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 110:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 111:
# links(m, cache_dirs) = 0, ((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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ m = ROOT_INO, m ∈ cache_dirs, ∀ ino. (ino ∈ ((cache_files ⊕ cache_pcache) ⊕ cache_icache) -- m ↔ ino ∈ ((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m)) ∧ ( ino ∈ ((cache_files ⊕ cache_pcache) ⊕ cache_icache) -- m → (((cache_files ⊕ cache_pcache) ⊕ cache_icache) -- m)[ino] = (((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m))[ino])

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files, files0] → [((cache_files ⊕ cache_pcache) ⊕ cache_icache) -- m, ((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m)] flags: <all paths>

Additional information

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