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Proof step 16 from proof refine-readdir (previous step)

cache_dirs[m] = mkdir(m3, md0, # links(m, cache_dirs), m5, entries), 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) ⊦ ⟨afs_readdir#(mkinode(m, md, boolvar, m0, m1, m2), cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; strings1, err0)⟩ (dom entries = strings1 ∧ ESUCCESS = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 17:
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)

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_readdir#(INODE, DIRS, FILES, ASYNCED; NAMES, ERR) {if pre-readdir(INODE.ino, DIRS, FILES) then { {NAMES := dom DIRS[INODE.ino].entries; ERR := ESUCCESS} or {choose NAMES0 with true in NAMES := NAMES0; fail#(; ; ERR)}} else abort };