[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 131 from proof refine-iget (previous step)

cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))][ino0] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), cache_files[ino] = mkfile(m, md, # links(ino, cache_dirs), content), cache_files[ino0] = mkfile(m4, md1, # links(ino0, cache_dirs), content0), 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), ino ∈ cache_files, ino0 ∈ cache_files, ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))], cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile(m3, md0, m1, content0 ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_icache, ino ∈ cache_dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 132:
⊦ 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)
Proof step 133:
cache_files[ino0] = mkfile(m4, md1, # links(ino0, cache_dirs), content0), cache_files[ino] = mkfile(m, md, # links(ino, cache_dirs), content), cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))][ino0] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), 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, false, # links(ino, cache_dirs), 0, m))], ino0 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile(m3, md0, m1, content0 ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_dirs, ino ∈ cache_icache, ino0 ∈ cache_icache ∧ ¬ cache_icache[ino0].inode.directory

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) Used terms: ino0, cache_icache, cache_files ⊕ cache_pcache