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Proof step 17 from proof refine-readdir (previous step)

asynced ↔ cache_asynced, cache_dirs[m] = mkdir(m3, md0, # links(m, cache_dirs), m5, entries), dirs = cache_dirs, err = err0, files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, inode = mkinode(m, md, boolvar, m0, m1, m2), strings0 = strings1, 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), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨if pre-readdir(inode.ino, dirs, files) then {{strings0 := dom dirs[inode.ino].entries; err := ESUCCESS} or {choose strings with true in strings0 := strings; fail#(; ; err)}} else abort⟩ (dom entries = strings0 ∧ ESUCCESS = err)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 18:
asynced ↔ cache_asynced, cache_dirs[m] = mkdir(m3, md0, # links(m, cache_dirs), m5, entries), dirs = cache_dirs, err = err0, files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, inode = mkinode(m, md, boolvar, m0, m1, m2), strings0 = strings1, 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), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨{strings0 := dom dirs[inode.ino].entries; err := ESUCCESS} or {choose strings with true in strings0 := strings; fail#(; ; err)}⟩ (dom entries = strings0 ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ pre-readdir(ino, dirs, files) ↔ valid-dir-ino(ino, dirs, files); (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)