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Proof step 243 from proof refine-mkdir (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m] = mkdir(cache_dirs[m].size, md1, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent = negdentry(str), p_inode = mkinode(m, md0, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), p_inode0 = mkinode(m, md0, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), 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, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ∃ ino. (¬ ino ∈ cache_dirs ∧ ¬ ino ∈ afs_files ∧ ino ≠ 0) ∧ ⟨afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, cache_dirs); afs_inode_sync#(p_inode; cache_dirs, afs_files); p_inode := (p_inode.ino ∈ cache_dirs ⊃ mkinode (p_inode.ino, cache_dirs[p_inode.ino].meta, true, cache_dirs[p_inode.ino].nlink, cache_dirs[p_inode.ino].nsubdirs, cache_dirs[p_inode.ino].size) ;mkinode(p_inode.ino, afs_files[p_inode.ino].meta, false, afs_files[p_inode.ino].nlink, 0, afs_files[p_inode.ino].size) ); c_inode := getinode(dent.ino, cache_dirs, afs_files); asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode0 = p_inode ∧ p_inode1 = c_inode ∧ negdentry(str) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), str ∈ cache_dirs[m].entries, str ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 244:
# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m] = mkdir(cache_dirs[m].size, md1, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_dirs0 = cache_dirs, dent = negdentry(str), p_inode = mkinode(m, md0, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), 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, ⌊err0⌋ , ¬ str ∈ entries, ¬ str ∈ cache_dirs[m].entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), ∃ ino. ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ cache_files ∧ ino ≠ 0 ∧ ⟨afs_mkdir_ino#(m, md, ino; dent, err, cache_dirs); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_inode_sync#(p_inode; cache_dirs, afs_files); p_inode2 := (p_inode.ino ∈ cache_dirs ⊃ mkinode (p_inode.ino, cache_dirs[p_inode.ino].meta, true, cache_dirs[p_inode.ino].nlink, cache_dirs[p_inode.ino].nsubdirs, cache_dirs[p_inode.ino].size) ;mkinode(p_inode.ino, afs_files[p_inode.ino].meta, false, afs_files[p_inode.ino].nlink, 0, afs_files[p_inode.ino].size) ); c_inode := getinode(dent.ino, cache_dirs, afs_files); asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode = p_inode2 ∧ p_inode1 = c_inode ∧ negdentry(str) = dent ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)