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Proof step 98 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), cache_files[m] = mkfile(m0, md0, 0, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, m ≠ ROOT_INO, 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_files, ¬ m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ⟨afs_evict#(mkinode(m, md, false, 0, 0, m2), cache_asynced; err0, cache_dirs, afs_files)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = ((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m) ∧ ESUCCESS = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 99:
# links(m, cache_dirs) = 0, asynced ↔ cache_asynced, cache_files[m] = mkfile(m0, md0, 0, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m1, md1, 0, content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, inode = mkinode(m, md, false, 0, 0, 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ cache_pcache → key.data? ⊦ ⟨if pre-evict(inode, dirs, files) then {err := ESUCCESS; let ino = inode.ino in if ino ∈ dirs then if dirs[ino].nlink = 0 then dirs := dirs -- ino else if files[ino].nlink = 0 then files := files -- ino} else abort⟩ (dirs = cache_dirs0 ∧ files = ((cache_files -- m) ⊕ evict(m, cache_pcache)) ⊕ (cache_icache -- m) ∧ ESUCCESS = err), m = ROOT_INO, m ∈ cache_dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_evict#(INODE, ASYNCED; ERR, DIRS, FILES) {if pre-evict(INODE, DIRS, FILES) then {ERR := ESUCCESS; let INO = INODE.ino in if INO ∈ DIRS then if DIRS[INO].nlink = 0 then DIRS := DIRS -- INO else if FILES[INO].nlink = 0 then FILES := FILES -- INO} else abort };