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Proof step 402 from proof refine-rename-dir-negdentry (previous step)

cache_dirs[m3] = mkdir(m1, md4, # links(m3, cache_dirs), m5, entries1), cache_dirs[m] = mkdir(m0, md3, # links(m, cache_dirs), m2, entries0), cache_dirs[entries1[str]] = mkdir(m4, md2, # links(entries1[str], cache_dirs), m7, entries), cache_dirs0[entries1[str]] = mkdir(m6, md5, m8, m9, entries2), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, new_child_inode1 = new_child_inode0, new_dent0 = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), new_parent_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), old_child_inode0 = mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs), m7, m4), old_dent0 = mkdentry(str, entries1[str]), old_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), old_parent_inode0 = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), 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, m3 ∈ cache_dirs, entries1[str] ∈ cache_dirs, str ∈ entries1, ⌊err0⌋ , 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 ⊦ ⟨afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err1, cache_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs0), m9, m6) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ mkdentry(str, entries1[str]) = old_dent0 ∧ negdentry(str0) = new_dent0 ∧ err0 = err1 ∧ cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced)), str0 ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 403:
cache_dirs[entries1[str]] = mkdir(m6, md5, # links(entries1[str], cache_dirs), m9, entries2), cache_dirs[m] = mkdir(m0, md3, # links(m, cache_dirs), m2, entries0), cache_dirs[m3] = mkdir(m1, md4, # links(m3, cache_dirs), m5, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, new_child_inode1 = new_child_inode0, new_dent0 = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), new_parent_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), old_child_inode0 = mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs), m9, m6), old_dent0 = mkdentry(str, entries1[str]), old_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), old_parent_inode0 = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), 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 ∈ entries1, entries1[str] ∈ cache_dirs, m3 ∈ cache_dirs, m ∈ cache_dirs, ⌊err0⌋ , ¬ str0 ∈ entries0, 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 ⊦ ⟨afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err1, cache_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs0), m9, m6) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ mkdentry(str, entries1[str]) = old_dent0 ∧ negdentry(str0) = new_dent0 ∧ err0 = err1 ∧ 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)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base