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Proof step 9 from proof refine-readdir (previous step)

asynced ↔ cache_asynced, dirs = cache_dirs, err = err0, files = cache_files, inode = mkinode(m, md, boolvar, m0, m1, m2), strings = strings1, strings0 = strings, 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) ⊦ ⟪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⟫ ⟨afs_readdir#(mkinode(m, md, boolvar, m0, m1, m2), cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; strings1, err0)⟩ (strings0 = strings1 ∧ err = err0)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 10:
asynced ↔ cache_asynced, dirs = cache_dirs, err = err0, files = cache_files, inode = mkinode(m, md, boolvar, m0, m1, m2), strings = strings1, strings0 = strings, 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) ⊦ ⟪{strings0 := dom dirs[inode.ino].entries; err := ESUCCESS} or {choose strings with true in strings0 := strings; fail#(; ; err)}⟫ ⟨afs_readdir#(mkinode(m, md, boolvar, m0, m1, m2), cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; strings1, err0)⟩ (strings0 = strings1 ∧ err = err0)

Rule argument

pos: right 1

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)