[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 97 from proof refine-create (previous step)

cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), dirs = cache_dirs[m1, mkdir(m2 + 1, md1, # links(m1, cache_dirs), m5, entries0[str, m])], files = (((cache_files ⊕ cache_pcache) ⊕ cache_icache) ++ m)[m, mkfile(0, md0, 1, ∅)], inode = mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2), 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), m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta; p_inode := (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, files[m1].meta, false, files[m1].nlink, 0, files[m1].size) ); c_inode := getinode(mkdentry(str, m).ino, dirs, files); asynced := ?⟩ ( dirs = cache_dirs[m1, mkdir(m2 + 1, md2, # links(m1, cache_dirs), m5, entries0[str, m])] ∧ files = ((cache_files ++ m)[m, mkfile(0, md0, 1, ∅)] ⊕ cache_pcache) ⊕ 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)) ] ∧ (asynced ↔ asynced0) ∧ mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1) = p_inode ∧ mkinode(m, md0, false, 1, 0, 0) = c_inode), m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Heuristic symbolic execution applied rule let right

And obtained the following new goals

Rule argument

Additional information