| # links (entries[str], cache_dirs [m8, (m8 = m14 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str)).meta:= md0 ] [m14, (m14 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).meta:= md5 ]) = # links(entries[str], cache_dirs), (m8 = m14 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs), m5, entries -- str)) = mkdir(m, md, m12, m13, entries0), (m14 = m8 ⊃ mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str);mkdir(m7, md7, # links(m14, cache_dirs), m11, entries2)) = mkdir(m0, md6, m4, m6, entries1), cache_files[entries[str]] = mkfile(m2, md3, # links(entries[str], cache_dirs), content0), cache_dirs[m14] = mkdir(m7, md7, # links(m14, cache_dirs), m11, entries2), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m9, md2, # links(entries[str], cache_dirs), content), cache_dirs[m8] = mkdir(m1 + 1, md4, # links(m8, cache_dirs), m5, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, new_child_inode = new_child_inode0, new_child_inode1 = new_child_inode0, new_dent = new_dent0, new_dent0 = negdentry(str0), new_parent_inode = new_parent_inode0, new_parent_inode0 = mkinode(m14, md5, true, # links(m14, cache_dirs), m11, m7), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10), old_dent = old_dent0, old_dent0 = mkdentry(str, entries[str]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m8, md0, true, # links(m8, cache_dirs), m5, m1 + 1), afs-cons (cache_dirs [m8, (m8 = m14 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str)).meta:= md0 ] [m14, (m14 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], cache_files), 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), m8 ∈ cache_dirs, m14 ∈ cache_dirs, entries[str] ∈ cache_files, str ∈ entries, m14 = m8 → md5 = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m14, cache_dirs) ≠ ∅ ∨ m14 = ROOT_INO, links(m8, cache_dirs) ≠ ∅ ∨ m8 = ROOT_INO ⊦ pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), entries[str] ∈ cache_dirs, str0 ∈ entries2 |
Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ ¬ negdentry(str).dentry?; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ negdentry(str).negdentry?; (s)% ⊦ negdentry(str).name = str; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)