| (m3 = m14 ⊃ mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0);mkdir(m2, md4, # links(m3, cache_dirs), m5, entries)) = mkdir(m8, md3, m10, m11, entries2), (entries[str] = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;(entries[str] = m14 ⊃ mkdir(m0, md5, # links(entries[str], cache_dirs), m1, entries0 -- str0) ;mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅) ) ) = mkdir(m13, md8, m12 + 1, m15, entries4), asynced ↔ false, cache_dirs[entries0[str0]] = mkdir(m6, md6, # links(entries0[str0], cache_dirs), m9, entries3), cache_dirs[entries[str]] = mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅), cache_dirs[m3] = mkdir(m2, md4, # links(m3, cache_dirs), m5, entries), cache_dirs[m14] = mkdir(m0 + 1, md5, # links(m14, cache_dirs), m1 + 1, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, icache = cache_icache, inode = ( m14 ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ mkinode (m14, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .meta, true, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .nlink, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .nsubdirs, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .size) ;mkinode(m14, cache_files[m14].meta, false, cache_files[m14].nlink, 0, cache_files[m14].size) ), 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), entries[str] ∈ cache_dirs, str0 ∈ entries0, str ∈ entries, m3 ∈ cache_dirs, entries0[str0] ∈ cache_dirs, m14 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m14 → md = md0, (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true)), (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0)), ( m14 ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ ( ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries) ∧ ( ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries) ∧ ( ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries) ∧ ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ;true ), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m14, cache_dirs) ≠ ∅ ∨ m14 = ROOT_INO ⊦ [icache[inode.ino] := mkientry(asynced, inode); icache_set# (( m3 ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ mkinode (m3, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .meta, true, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .nlink, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .nsubdirs, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ), false ; err, icache); new_child_inode := ( entries[str] ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ mkinode (entries[str], cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .meta, true, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .nlink, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .nsubdirs, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .size) ;mkinode(entries[str], cache_files[entries[str]].meta, false, cache_files[entries[str]].nlink, 0, cache_files[entries[str]].size) ); entries1 := entries; cache_icache := icache; if mkdentry(str, entries1[str]).dentry? then icache_set#(new_child_inode, false; err, cache_icache); dcache_delete#(m14, mkdentry(str0, entries0[str0]).name; err, cache_dcache); dcache_set# (m3, mkdentry(mkdentry(str, entries[str]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str, entries[str]).name, mkdentry(str0, entries0[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ dcache-cons (cache_dcache, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ pcache-cons (cache_pcache, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ afs-cons (cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ synced (cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries1[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m3, md, true, # links(m3, cache_dirs), m5, m2); old_parent_inode0 := mkinode(m14, md0, true, # links(m14, cache_dirs), m1 + 1, m0 + 1); new_child_inode0 := mkinode (entries1[str], md1, true, # links(entries1[str], cache_dirs), cache_dirs[entries1[str]].nsubdirs, cache_dirs[entries1[str]].size); old_child_inode0 := mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m9, m6); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; cache_dirs5 := 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)⟩ ( (m14 ∈ cache_dirs5 ⊃ mkinode (m14, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .meta, true, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .nlink, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .nsubdirs, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .size) ;mkinode(m14, cache_files[m14].meta, false, cache_files[m14].nlink, 0, cache_files[m14].size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs5 ⊃ mkinode (m3, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .meta, true, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .nlink, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .nsubdirs, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) = new_parent_inode0 ∧ mkinode (entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), cache_dirs1[entries0[str0]].nsubdirs, cache_dirs2[entries0[str0]].size) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str, entries0[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs5 [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ∧ entries[str] ∈ cache_dirs5 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ∧ entries[str] ∈ cache_dirs5 ⊃ mkdir(m13, md0, m12, m15, entries4) ;(entries[str] ∈ cache_dirs5 ⊃ mkdir(m13, md8, m12, m15, entries4);cache_dirs5[entries[str]]) ) ) .meta:= md1 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0))), entries[str] = ROOT_INO, m14 = m3 ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0]) |
(entries[str] = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;(entries[str] = m14 ⊃ mkdir(m0, md5, # links(entries[str], cache_dirs), m1, entries0 -- str0) ;mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅) ) ) = mkdir(m13, md8, m12 + 1, m15, entries4), (m3 = m14 ⊃ mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0);mkdir(m2, md4, # links(m3, cache_dirs), m5, entries)) = mkdir(m8, md3, m10, m11, entries2), asynced ↔ false, cache_dirs[m14] = mkdir(m0 + 1, md5, # links(m14, cache_dirs), m1 + 1, entries0), cache_dirs[m3] = mkdir(m2, md4, # links(m3, cache_dirs), m5, entries), cache_dirs[entries[str]] = mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅), cache_dirs[entries0[str0]] = mkdir(m6, md6, # links(entries0[str0], cache_dirs), m9, entries3), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, icache = icache0[inode.ino, mkientry(asynced, inode)], icache0 = cache_icache, inode = ( m14 ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ mkinode (m14, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .meta, true, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .nlink, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .nsubdirs, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= md1 ] [m14 ] .size) ;mkinode(m14, cache_files[m14].meta, false, cache_files[m14].nlink, 0, cache_files[m14].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), m14 ∈ cache_dirs, entries0[str0] ∈ cache_dirs, m3 ∈ cache_dirs, str ∈ entries, str0 ∈ entries0, entries[str] ∈ cache_dirs, m3 = m14 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), ( m14 ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ ( ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries) ∧ ( ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries) ∧ ( ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries) ∧ ( (str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ∧ ( (str ∈ entries ∧ str ∈ entries ∧ (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true))) ∧ (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0))) ∧ str ∈ entries ;true ), (m3 = m14 ⊃ str ∈ entries ∧ (m14 = entries[str] ⊃ true;str0 ∈ entries0);str ∈ entries ∧ (m3 = entries[str] ⊃ true;str0 ∈ entries0)), (m14 = entries[str] ⊃ true;(m14 = m3 ⊃ str0 ∈ entries0;true)), links(m14, cache_dirs) ≠ ∅ ∨ m14 = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [icache_set# (( m3 ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ mkinode (m3, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .meta, true, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .nlink, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .nsubdirs, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [m3 ] .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ), false ; err, icache); new_child_inode := ( entries[str] ∈ cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] ⊃ mkinode (entries[str], cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .meta, true, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .nlink, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .nsubdirs, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str] ] .meta:= mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4).meta ] [entries[str] ] .size) ;mkinode(entries[str], cache_files[entries[str]].meta, false, cache_files[entries[str]].nlink, 0, cache_files[entries[str]].size) ); entries1 := entries; cache_icache := icache; if mkdentry(str, entries1[str]).dentry? then icache_set#(new_child_inode, false; err, cache_icache); dcache_delete#(m14, mkdentry(str0, entries0[str0]).name; err, cache_dcache); dcache_set# (m3, mkdentry(mkdentry(str, entries[str]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str, entries[str]).name, mkdentry(str0, entries0[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ dcache-cons (cache_dcache, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ pcache-cons (cache_pcache, cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ afs-cons (cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_files) ∧ synced (cache_dirs [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)) ) .meta:= md1 ], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries1[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m3, md, true, # links(m3, cache_dirs), m5, m2); old_parent_inode0 := mkinode(m14, md0, true, # links(m14, cache_dirs), m1 + 1, m0 + 1); new_child_inode0 := mkinode (entries1[str], md1, true, # links(entries1[str], cache_dirs), cache_dirs[entries1[str]].nsubdirs, cache_dirs[entries1[str]].size); old_child_inode0 := mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m9, m6); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; cache_dirs5 := 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)⟩ ( (m14 ∈ cache_dirs5 ⊃ mkinode (m14, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .meta, true, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .nlink, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .nsubdirs, (m14 = entries[str] ⊃ (entries[str] = m3 ⊃ mkdir(m13, md, m12, m15, entries4);mkdir(m13, md0, m12, m15, entries4)).meta:= md1 ;(m14 = m3 ⊃ mkdir(m8, md, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md0, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .size) ;mkinode(m14, cache_files[m14].meta, false, cache_files[m14].nlink, 0, cache_files[m14].size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs5 ⊃ mkinode (m3, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .meta, true, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .nlink, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .nsubdirs, (m3 = entries[str] ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md.meta:= md1 ; (m3 = m14 ⊃ mkdir(m8, md0, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ) .meta:= md ) .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) = new_parent_inode0 ∧ mkinode (entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), cache_dirs1[entries0[str0]].nsubdirs, cache_dirs2[entries0[str0]].size) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str, entries0[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs5 [m14, (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m14 = m3 ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;mkdir(m0, md5, # links(m14, cache_dirs5), m1, entries0 -- str0) ) ) .meta:= md0 ] [m3, (m3 = m14 ⊃ (m14 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) .meta:= md0 ;(m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ] [entries[str], (entries[str] = m3 ∧ entries[str] ∈ cache_dirs5 ⊃ (entries[str] = m14 ⊃ mkdir(m13, md0, m12, m15, entries4);mkdir(m13, md8, m12, m15, entries4)).meta:= md ;(entries[str] = m14 ∧ entries[str] ∈ cache_dirs5 ⊃ mkdir(m13, md0, m12, m15, entries4) ;(entries[str] ∈ cache_dirs5 ⊃ mkdir(m13, md8, m12, m15, entries4);cache_dirs5[entries[str]]) ) ) .meta:= md1 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0))), entries[str] = ROOT_INO, m14 = m3 ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0])