[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 21 from proof inv-link (previous step)

dirs[ino] = mkdir(m2, md3, # links(ino, dirs), m6, entries0), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[m] = mkdir(m1, md2, # links(m, dirs), m4, entries), c_inode = mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3), new_dent = negdentry(str0), old_dent = mkdentry(str, entries0[str]), p_ino = p_inode.ino, p_inode = mkinode(m, md, true, # links(m, dirs), m4, m1), old_dent.dentry?, afs-cons(dirs, files), pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files), entries0[str] ∈ files, m ∈ dirs, str ∈ entries0, ino ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪dirs := dirs[p_ino, dirs[p_ino].entries:= dirs[p_ino].entries[new_dent.name, old_dent.ino]] [p_ino, dirs[p_ino, dirs[p_ino].entries:= dirs[p_ino].entries[new_dent.name, old_dent.ino]][p_ino] .size:= (dirs[p_ino, dirs[p_ino].entries:= dirs[p_ino].entries[new_dent.name, old_dent.ino]][p_ino].size + 1) ]; let ino = old_dent.ino in afs_inc_nlink#(ino; dirs, files); new_dent := mkdentry(new_dent.name, old_dent.ino); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(old_dent.ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ entries

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 22:
dirs[m] = mkdir(m1, md2, # links(m, dirs), m4, entries), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[ino] = mkdir(m2, md3, # links(ino, dirs), m6, entries0), c_inode = mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3), new_dent = negdentry(str0), old_dent = mkdentry(str, entries0[str]), p_ino = p_inode.ino, p_inode = mkinode(m, md, true, # links(m, dirs), m4, m1), old_dent.dentry?, afs-cons(dirs, files), pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files), ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries0[str] ∈ files, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪let ino = old_dent.ino in {dirs := dirs[p_ino, dirs[p_ino].entries:= dirs[p_ino].entries[new_dent.name, old_dent.ino]] [p_ino, dirs[p_ino, dirs[p_ino].entries:= dirs[p_ino].entries[new_dent.name, old_dent.ino]][p_ino] .size:= (dirs[p_ino, dirs[p_ino].entries:= dirs[p_ino].entries[new_dent.name, old_dent.ino]][p_ino].size + 1) ]; afs_inc_nlink#(ino; dirs, files)}; new_dent := mkdentry(new_dent.name, old_dent.ino); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(old_dent.ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ entries

Rule argument

Additional information

Used simplifier rules: ⊦ pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ↔ valid-dentry(old_dent, dirs, files) ∧ valid-negdentry(p_inode.ino, new_dent, dirs, files) ∧ (links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO) ∧ valid-dir-inode(p_inode, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ c_inode.ino = old_dent.ino; (s)%⊦ valid-dentry(dent, dirs, files) ↔ (∃ ino. valid-dentry(ino, dent, dirs, 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)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ negdentry(str).name = str; (s)% ⊦ negdentry(str).negdentry?; (s)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], 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)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (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-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)