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Proof step 335 from proof refine-rename-file-negdentry (previous step)

# links(m3, cache_dirs) = m5, cache_files[entries1[str]] = mkfile(m1, md3, # links(entries1[str], cache_dirs), content0), cache_dirs[m] = mkdir(m0, md4, # links(m, cache_dirs), m4, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m9, md2, # links(entries1[str], cache_dirs), content), cache_dirs[m3] = mkdir(m2, md6, m5, m6, entries1), entries1[str] = entries0[str], cache_dirs[m3] = mkdir(m2, md5, m5, m6, 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), str ∈ entries1, m ∈ cache_dirs, entries1[str] ∈ cache_files, m3 ∈ cache_dirs, str ∈ entries0, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪old_parent_inode := mkinode(m3, md0, true, m5, m6, m2); old_dent := mkdentry(str, entries1[str]); new_parent_inode := mkinode(m, md, true, # links(m, cache_dirs), m4, m0); new_dent := negdentry(str0); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); skip; dcache_delete#(old_parent_inode.ino, old_dent.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}⟫ ⟨old_dent0 := mkdentry(str, entries1[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m4, m0); old_parent_inode0 := mkinode(m3, md0, true, # links(m3, cache_dirs), m6, m2); old_child_inode0 := mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10); new_child_inode1 := new_child_inode0; cache_dirs0 := cache_dirs; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs0), 0, m10) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced)), str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 336:
cache_dirs[m3] = mkdir(m2, md5, # links(m3, cache_dirs), m6, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, # links(entries0[str], cache_dirs), content), cache_dirs[m] = mkdir(m0, md4, # links(m, cache_dirs), m4, entries), cache_files[entries0[str]] = mkfile(m1, md3, # links(entries0[str], cache_dirs), content0), 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), m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, ¬ str0 ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪old_parent_inode := mkinode(m3, md0, true, # links(m3, cache_dirs), m6, m2); old_dent := mkdentry(str, entries0[str]); new_parent_inode := mkinode(m, md, true, # links(m, cache_dirs), m4, m0); new_dent := negdentry(str0); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); skip; dcache_delete#(old_parent_inode.ino, old_dent.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}⟫ ⟨old_dent0 := mkdentry(str, entries0[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m4, m0); old_parent_inode0 := mkinode(m3, md0, true, # links(m3, cache_dirs), m6, m2); old_child_inode0 := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); new_child_inode1 := new_child_inode0; cache_dirs0 := cache_dirs; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs0), 0, m10) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced))

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)