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Proof step 91 from proof refine-iget (previous step)

cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0] = mkientry(boolvar, mkinode(m0, md0, true, m2, m3, m4)), cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), cache_files[ino0] = mkfile(m5, md1, # links(ino0, cache_dirs), content), 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), ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))], ino ∈ cache_dirs, ino0 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile(m5, md1, # links(ino0, cache_dirs), content ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [ino0, cache_icache, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ icache ∧ ¬ ino0 ∈ icache → icache[ino0, ie][ino] = icache[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).content = content; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s) Used terms: ino0, cache_icache, cache_files ⊕ cache_pcache