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Proof step 16 from proof refine-rename-file-negdentry (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m3].entries[str]] = mkfile(m9, md2, m11, content), cache_dirs[m] = mkdir(m8, md3, m12, m13, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m0 = m12, m1 = m13, m2 = m8, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, m7 = cache_dirs[m3].entries[str], new_child_inode = new_child_inode0, new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, m12, m13, m8), old_child_inode = mkinode(cache_dirs[m3].entries[str], md1, false, m11, 0, m10), old_dent = mkdentry(str, cache_dirs[m3].entries[str]), old_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].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), str ∈ cache_dirs[m3].entries, m3 ∈ cache_dirs, cache_dirs[m3].entries[str] ∈ cache_files, m ∈ cache_dirs, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨old_dent0 := mkdentry(str, m7); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, m0, m1, m2); old_parent_inode0 := mkinode(m3, md0, true, m4, m5, m6); old_child_inode0 := mkinode(m7, md1, false, m11, 0, m10); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)), str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# links(m, cache_dirs) = m12, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m3].entries[str]] = mkfile(m9, md2, m11, content), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, m7 = cache_dirs[m3].entries[str], new_child_inode = new_child_inode0, new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m13, m8), old_child_inode = mkinode(cache_dirs[m3].entries[str], md1, false, m11, 0, m10), old_dent = mkdentry(str, cache_dirs[m3].entries[str]), old_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].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), str ∈ cache_dirs[m3].entries, m3 ∈ cache_dirs, cache_dirs[m3].entries[str] ∈ cache_files, m ∈ cache_dirs, ¬ str0 ∈ entries, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨old_dent0 := mkdentry(str, m7); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, m12, m13, m8); old_parent_inode0 := mkinode(m3, md0, true, m4, m5, m6); old_child_inode0 := mkinode(m7, md1, false, m11, 0, m10); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced))

Rule argument

Additional information

Used simplifier rules: 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