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Proof step 247 from proof refine-mkdir (previous step)

# links(m, cache_dirs) = m4, cache_dirs[m] = mkdir(m0, md1, m4, m5, entries), cache_dirs[m] = mkdir(m0, md0, m4, m5, entries0), cache_dirs0 = cache_dirs, dent = negdentry(str), m1 = m4, m2 = m5, m3 = m0, 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⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ∃ 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#(mkinode(m, md2, true, m1, m2, m3); cache_dirs, afs_files); p_inode2 := (m ∈ cache_dirs ⊃ mkinode(m, cache_dirs[m].meta, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size) ;mkinode(m, afs_files[m].meta, false, afs_files[m].nlink, 0, afs_files[m].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) ∧ mkinode(m, md2, true, m1, m2, m3) = p_inode2 ∧ p_inode1 = c_inode ∧ negdentry(str) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), str ∈ entries, str ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 248:
# links(m, cache_dirs) = m4, cache_dirs[m] = mkdir(m0, md0, # links(m, cache_dirs), m5, entries0), cache_dirs0 = cache_dirs, dent = negdentry(str), 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⌋ , ¬ str ∈ entries0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ∃ 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#(mkinode(m, md2, true, m4, m5, m0); cache_dirs, afs_files); p_inode2 := (m ∈ cache_dirs ⊃ mkinode(m, cache_dirs[m].meta, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size) ;mkinode(m, afs_files[m].meta, false, afs_files[m].nlink, 0, afs_files[m].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) ∧ mkinode(m, md2, true, m4, m5, m0) = p_inode2 ∧ p_inode1 = c_inode ∧ negdentry(str) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)