[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 326 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), 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 ⊦ pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ 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)