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Proof step 85 from proof refine-evict (previous step)

0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, cache_files[m] = mkfile(m0, md0, m1, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, m1 = 0, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_delete#(m; err, cache_icache); boolvar := false; if ¬ boolvar then pcache_evict#(m; err, cache_pcache)⟫ ⟨cache_dirs0 := cache_dirs; afs_evict#(mkinode(m, md, boolvar, 0, 0, m2), cache_asynced; err0, cache_dirs, afs_files)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = ((cache_files -- m) ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0), m = ROOT_INO, m ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base