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Proof step 36 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_dirs[m] = mkdir(m0, md0, 0, m2, entries), 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_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m = ROOT_INO, (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ (cache_icache -- m)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 38:
# links(m, cache_dirs) = 0, cache_dirs[m] = mkdir(m0, md0, 0, m2, entries), 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_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m = ROOT_INO, ∀ ino. (ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache ↔ ino ∈ (cache_files ⊕ cache_pcache) ⊕ (cache_icache -- m)) ∧ ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache → ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ 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, (cache_files ⊕ cache_pcache) ⊕ (cache_icache -- m)] flags: <all paths>

Additional information

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