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Proof step 48 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_dirs[m] = mkdir(m0, md0, 0, m2, entries), cache_icache[ino] = mkientry(boolvar0, mkinode(m1, 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), ino ∈ cache_files, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache) ⊕ (cache_icache -- m))[ino], ino = m, m = ROOT_INO, ¬ boolvar ∧ ino ∈ cache_icache, ino ∈ cache_icache ∧ boolvar

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-icache-overwrite-not-cached seq: ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [ino, cache_icache -- m, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ino ∈ icache -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ icache; (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s) Used terms: ino, cache_icache -- m, cache_files ⊕ cache_pcache