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Proof step 18 from proof refine-evict (previous step)

dirs[ino].nlink = 0, asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs, err = ESUCCESS, err1 = err0, files = cache_files, ino = inode.ino, inode = mkinode(m, md, boolvar, m0, m1, m2), m0 = 0, 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), ino ∈ dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = cache_files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar, m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪icache_delete#(m; err, cache_icache); if ¬ boolvar then pcache_evict#(m; err, cache_pcache)⟫ ⟨afs_evict#(mkinode(m, md, boolvar, m0, m1, m2), cache_asynced; err0, afs_dirs, afs_files)⟩ (afs_dirs = dirs -- ino ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0), m = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
cache_dirs[m].nlink = 0, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, m ≠ ROOT_INO, 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) ⊦ ⟪icache_delete#(m; err, cache_icache); boolvar := true; if ¬ boolvar then pcache_evict#(m; err, cache_pcache)⟫ ⟨cache_dirs0 := cache_dirs; afs_evict#(mkinode(m, md, boolvar, 0, cache_dirs[m].nsubdirs, cache_dirs[m].size), cache_asynced; err0, cache_dirs, afs_files)⟩ (cache_dirs = cache_dirs0 -- m ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)