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Proof step 137 from proof refine-create (previous step)

cache_files[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))][ino] = mkientry(boolvar0, mkinode(m0, md, true, m3, m4, m6)), cache_icache[ino] = mkientry(boolvar1, mkinode(m8, md4, boolvar, m9, m10, m11)), 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), m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ], ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)), m = 0, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0, ino ∈ cache_icache ∧ ¬ boolvar, 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, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s) Used terms: ino, cache_icache, cache_files ⊕ cache_pcache