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Proof step 298 from proof refine-rmdir (previous step)

# links(entries[str], cache_dirs) = m3, cache_dirs[m] = mkdir(m0 + 1, md2, # links(m, cache_dirs), m1 + 1, entries), cache_dirs[entries[str]] = mkdir(m2, md3, m3, m4, ∅), cache_dirs[entries[str]] = mkdir(m2, md1, m3, m4, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m0, md2, # links(m, cache_dirs), m1, entries -- str)], entries0 = ∅, 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), entries[str] ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, afs_files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); dirs, afs_files); afs_inode_sync#(mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2); dirs, afs_files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, afs_files[m].meta, false, afs_files[m].nlink, 0, afs_files[m].size) ); c_inode := getinode(entries[str], dirs, afs_files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1) = p_inode ∧ mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2) = c_inode ∧ mkdentry(str, entries[str]) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 299:
cache_dirs[entries[str]] = mkdir(m2, md1, # links(entries[str], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0 + 1, md2, # links(m, cache_dirs), m1 + 1, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m0, md2, # links(m, cache_dirs), m1, entries -- str)], entries[str] ≠ 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), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_dirs, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, afs_files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); dirs, afs_files); afs_inode_sync#(mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2); dirs, afs_files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, afs_files[m].meta, false, afs_files[m].nlink, 0, afs_files[m].size) ); c_inode := getinode(entries[str], dirs, afs_files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1) = p_inode ∧ mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2) = c_inode ∧ mkdentry(str, entries[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)