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Proof step 154 from proof refine-rename-dir-negdentry (previous step)

(m16 = m9 ⊃ mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str);mkdir(m6, md6, # links(m16, cache_dirs), m8, entries3)) = mkdir(m2, md2, m4, m5, entries), (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) = mkdir(m, md, m11, m12, entries2), (m16 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) = mkdir(m13, md7, m14, m15, entries4), cache_dirs[entries0[str]] = mkdir(m3, md8, # links(entries0[str], cache_dirs), m18, entries5), cache_dirs[m16] = mkdir(m6, md6, # links(m16, cache_dirs), m8, entries3), cache_dirs[m9] = mkdir(m0 + 1, md3, # links(m9, cache_dirs), m1 + 1, entries0), 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(m16, md5, true, # links(m16, cache_dirs), m8, m6), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs), m18, m3), old_dent = old_dent0, old_dent0 = mkdentry(str, entries0[str]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m9, md0, true, # links(m9, cache_dirs), m1 + 1, m0 + 1), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), dcache-cons ((cache_dcache -- dentrykey(m9, str))[dentrykey(m16, str0), mkdentry(str0, entries0[str])], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), synced (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, entries0[str] ∈ cache_dirs, m9 ∈ cache_dirs, m16 ∈ cache_dirs, cache_sync → synced (cache_files, cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), m16 = m9 → md5 = md0, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(m16, cache_dirs) ≠ ∅ ∨ m16 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( (m9 ∈ cache_dirs0 ⊃ mkinode (m9, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta, true, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nlink, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nsubdirs, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .size) ;mkinode(m9, cache_files[m9].meta, false, cache_files[m9].nlink, 0, cache_files[m9].size) ) = old_parent_inode ∧ (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) ) = new_parent_inode ∧ mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs0), m18, m3) = old_child_inode ∧ new_child_inode1 = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str0, entries0[str]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0 [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta:= md0 ] [m16, (m16 = m9 ∧ m9 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;(m16 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);cache_dirs0[m16]) ) .meta:= md5 ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [m16, mkientry (false, (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) )) ] ∧ (asynced ↔ asynced0)), ⟨let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, asynced1 = new_dent.dentry? in let asynced0 = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; if ¬ asynced0 then {dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1}; dirs[new_ino].entries[new_dent.name] := old_dent.ino; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS}; asynced := ?⟩ ( (m9 ∈ cache_dirs0 ⊃ mkinode (m9, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta, true, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nlink, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nsubdirs, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .size) ;mkinode(m9, cache_files[m9].meta, false, cache_files[m9].nlink, 0, cache_files[m9].size) ) = old_parent_inode ∧ (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) ) = new_parent_inode ∧ mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs0), m18, m3) = old_child_inode ∧ new_child_inode1 = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str0, entries0[str]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0 [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta:= md0 ] [m16, (m16 = m9 ∧ m9 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;(m16 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);cache_dirs0[m16]) ) .meta:= md5 ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [m16, mkientry (false, (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) )) ] ∧ (asynced ↔ asynced0)), str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 155:
# links(entries0[str], cache_dirs) = cache_dirs[entries0[str]].nlink, # links(m16, cache_dirs) = cache_dirs[m16].nlink, # links(m9, cache_dirs) = cache_dirs[m9].nlink, m1 + 1 = cache_dirs[m9].nsubdirs, m0 + 1 = cache_dirs[m9].size, (m16 = m9 ⊃ mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str);cache_dirs[m16]) = mkdir(m2, md2, m4, m5, entries), (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, cache_dirs[m9].nlink, m1, entries0 -- str)) = mkdir(m, md, m11, m12, entries2), (m16 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) = mkdir(m13, md7, m14, m15, entries4), entries0[str] = cache_dirs[m9].entries[str], cache_dirs[entries0[str]] = mkdir(cache_dirs[entries0[str]].size, md8, cache_dirs[entries0[str]].nlink, cache_dirs[entries0[str]].nsubdirs, entries5), cache_dirs[m16] = mkdir(cache_dirs[m16].size, md6, cache_dirs[m16].nlink, cache_dirs[m16].nsubdirs, entries3), cache_dirs[m9] = mkdir(m0 + 1, md3, cache_dirs[m9].nlink, m1 + 1, entries0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), dcache-cons ((cache_dcache -- dentrykey(m9, str))[dentrykey(m16, str0), mkdentry(str0, entries0[str])], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), str ∈ cache_dirs[m9].entries, str ∈ entries0, entries0[str] ∈ cache_dirs, m9 ∈ cache_dirs, m16 ∈ cache_dirs, ¬ str0 ∈ cache_dirs[m16].entries, ¬ str0 ∈ entries3, cache_sync → synced (cache_files, cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), m16 = m9 → md5 = md0, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(m16, cache_dirs) ≠ ∅ ∨ m16 = ROOT_INO ⊦ ⟨let old_ino = m9, new_ino = m16, asynced1 = false in let asynced0 = false in {dirs := cache_dirs[old_ino, cache_dirs[old_ino].entries:= (cache_dirs[old_ino].entries -- mkdentry(str, entries0[str]).name)]; old_dent := mkdentry(str, entries0[str]); if ¬ asynced0 then {dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1}; dirs[new_ino].entries[str0] := old_dent.ino; new_dent := negdentry(str0); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, afs_files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m9, md0, true, # links(m9, cache_dirs), m1 + 1, m0 + 1); dirs, afs_files); afs_inode_sync#(mkinode(m16, md5, true, # links(m16, cache_dirs), cache_dirs[m16].nsubdirs, cache_dirs[m16].size); dirs, afs_files); new_child_inode := new_child_inode0; 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 := (m9 ∈ dirs ⊃ mkinode(m9, dirs[m9].meta, true, dirs[m9].nlink, dirs[m9].nsubdirs, dirs[m9].size) ;mkinode(m9, afs_files[m9].meta, false, afs_files[m9].nlink, 0, afs_files[m9].size) ); new_parent_inode := (m16 ∈ dirs ⊃ mkinode(m16, dirs[m16].meta, true, dirs[m16].nlink, dirs[m16].nsubdirs, dirs[m16].size) ;mkinode(m16, afs_files[m16].meta, false, afs_files[m16].nlink, 0, afs_files[m16].size) ); err := ESUCCESS}; asynced := ?⟩ ( mkinode (m9, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) .meta, true, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) .nlink, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) .nsubdirs, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) .size) = old_parent_inode ∧ mkinode(m16, md5, true, m14, m15, m13) = new_parent_inode ∧ new_child_inode0 = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str0, entries0[str]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m16, (m16 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))] ∧ (asynced ↔ asynced0))

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%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkdentry(str, m) ≠ negdentry(str0); (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (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)