| (m = m3 ⊃ mkdir(m2, md2, # links(m3, cache_dirs), m6, entries1 -- str0);mkdir(m4, md8, # links(m, cache_dirs), m7, entries0)) = mkdir(m5, md7, m9, m11, entries), cache_files[entries0[str]] = mkfile(m1, md5, # links(entries0[str], cache_dirs), content2), cache_dirs[m3] = mkdir(m2 + 1, md2, # links(m3, cache_dirs), m6, entries1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m12, md3, # links(entries0[str], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str0]] = mkfile(m8, md4, # links(entries1[str0], cache_dirs), content0), cache_dirs[m] = mkdir(m4, md8, # links(m, cache_dirs), m7, entries0), cache_files[entries1[str0]] = mkfile(m0, md6, # links(entries1[str0], cache_dirs), content3), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m3, mkdir(m2, md2, # links(m3, cache_dirs), m6, entries1 -- str0)][m, mkdir(m5, md7, m9, m11, entries[str, entries1[str0]])], 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), entries1[str0] ∈ cache_files, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries0, str0 ∈ entries1, ⌊err1⌋ , ¬ entries1[str0] ∈ cache_dirs, ¬ entries0[str] ∈ 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 ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), ⟨afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, afs_files); old_dent := mkdentry(str0, entries1[str0]); asynced1 := true; if ¬ asynced1 then {dirs[m].size := dirs[m].size + 1; if old_dent.ino ∈ dirs then dirs[m].nsubdirs := dirs[m].nsubdirs + 1}; new_dent := mkdentry(mkdentry(str, entries0[str]).name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m3, md0, true, # links(m3, cache_dirs), m6, m2 + 1); dirs, afs_files); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m7, m4); dirs, afs_files); new_child_inode := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, afs_files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, afs_files[new_child_inode.ino].meta, false, afs_files[new_child_inode.ino].nlink, 0, afs_files[new_child_inode.ino].size) )}; old_parent_inode := (m3 ∈ dirs ⊃ mkinode(m3, dirs[m3].meta, true, dirs[m3].nlink, dirs[m3].nsubdirs, dirs[m3].size) ;mkinode(m3, afs_files[m3].meta, false, afs_files[m3].nlink, 0, afs_files[m3].size) ); new_parent_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) ); err := ESUCCESS; asynced := ?⟩ ( mkinode(m3, md0, true, # links(m3, cache_dirs), m6, m2 + 1) = old_parent_inode ∧ mkinode(m, md, true, # links(m, cache_dirs), m7, m4) = new_parent_inode ∧ mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10) = new_child_inode ∧ mkdentry(str0, entries1[str0]) = old_dent ∧ mkdentry(str, entries0[str]) = new_dent ∧ err1 = err ∧ dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced2)), ⟨err := err1; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), m3 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0]) |
(m = m3 ⊃ mkdir(m2, md2, # links(m3, cache_dirs), m6, entries1 -- str0);mkdir(m4, md8, # links(m, cache_dirs), m7, entries0)) = mkdir(m5, md7, m9, m11, entries), cache_files[entries1[str0]] = mkfile(m0, md6, # links(entries1[str0], cache_dirs), content3), cache_dirs[m] = mkdir(m4, md8, # links(m, cache_dirs), m7, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str0]] = mkfile(m8, md4, # links(entries1[str0], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m12, md3, # links(entries0[str], cache_dirs), content), cache_dirs[m3] = mkdir(m2 + 1, md2, # links(m3, cache_dirs), m6, entries1), cache_files[entries0[str]] = mkfile(m1, md5, # links(entries0[str], cache_dirs), content2), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m3, mkdir(m2, md2, # links(m3, cache_dirs), m6, entries1 -- str0)][m, mkdir(m5, md7, m9, m11, entries[str, entries1[str0]])], 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), str0 ∈ entries1, str ∈ entries0, m ∈ cache_dirs, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, entries1[str0] ∈ cache_files, ⌊err1⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟨asynced := ?⟩ (err1 = err1 ∧ (asynced ↔ asynced2)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), ⟨afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, afs_files); old_dent := mkdentry(str0, entries1[str0]); asynced1 := true; if ¬ asynced1 then {dirs[m].size := dirs[m].size + 1; if old_dent.ino ∈ dirs then dirs[m].nsubdirs := dirs[m].nsubdirs + 1}; new_dent := mkdentry(mkdentry(str, entries0[str]).name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m3, md0, true, # links(m3, cache_dirs), m6, m2 + 1); dirs, afs_files); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m7, m4); dirs, afs_files); new_child_inode := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, afs_files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, afs_files[new_child_inode.ino].meta, false, afs_files[new_child_inode.ino].nlink, 0, afs_files[new_child_inode.ino].size) )}; old_parent_inode := (m3 ∈ dirs ⊃ mkinode(m3, dirs[m3].meta, true, dirs[m3].nlink, dirs[m3].nsubdirs, dirs[m3].size) ;mkinode(m3, afs_files[m3].meta, false, afs_files[m3].nlink, 0, afs_files[m3].size) ); new_parent_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) ); err := ESUCCESS; asynced := ?⟩ ( mkinode(m3, md0, true, # links(m3, cache_dirs), m6, m2 + 1) = old_parent_inode ∧ mkinode(m, md, true, # links(m, cache_dirs), m7, m4) = new_parent_inode ∧ mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10) = new_child_inode ∧ mkdentry(str0, entries1[str0]) = old_dent ∧ mkdentry(str, entries0[str]) = new_dent ∧ err1 = err ∧ dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced2)), entries1[str0] ∈ cache_dirs, entries0[str] ∈ cache_dirs, m3 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])