[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 153 from proof inv-renam (previous step)

dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), dirs[entries0[str]] = mkdir(m, md, # links(entries0[str], dirs), m2, entries), dent = negdentry((q0 + str0 ').last), err = ESUCCESS, err0 = err, err1 = ESUCCESS, inode = getinode(ino, dirs, files), inode0 = mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0), p_inode = getinode(mkdentry(str, entries0[str]).ino, dirs, files), mkdentry(str, entries0[str]).dentry?, inode.directory, dom of < ino2, afs-cons(dirs, files), ispath(q0, ROOT_INO, ino, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pre-iget(ino, dirs, files), pw(user, md), pw(user, md0), px(user, md0), px(user, inode.meta), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ dirs, ino1 ∈ dirs, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪afs_lookup#(ino, dirs, files, asynced; dent, err0); if err0 = ENOENT then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err0) else if err0 = ESUCCESS then {isdir := true; vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err0)}; new_inode := inode; new_dent := dent; new_dent_inode := p_inode; if err0 = ESUCCESS then afs_check_commit#(dirs, files; err0; asynced); if err0 = ESUCCESS then let dent = new_dent in {old_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); old_dent := mkdentry(str, entries0[str]); old_dent_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err0, dirs, files; asynced); if dent.dentry? then vfs_put_inode#(new_dent_inode, of, asynced; err0, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), q0 + str0 ' = ε, entries0[str] = ROOT_INO, q + str ' ⊑ q0 + str0 '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 154:
dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), dirs[entries0[str]] = mkdir(m, md, # links(entries0[str], dirs), m2, entries), dent = negdentry(str0), err = ESUCCESS, entries0[str] ≠ ROOT_INO, dom of < ino2, afs-cons(dirs, files), ispath(q0, ROOT_INO, ino, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), pw(user, md0), px(user, md0), px(user, dirs[ino].meta), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ dirs, ino1 ∈ dirs, ino ∈ dirs, ¬ q + str ' ⊑ q0 + str0 ', links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪afs_lookup#(ino, dirs, files, asynced; dent, err); p_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); inode := (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) ); if err = ENOENT then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err) else if err = ESUCCESS then {isdir := true; vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}; new_inode := inode; new_dent := dent; new_dent_inode := p_inode; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then let dent = new_dent in {old_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); old_dent := mkdentry(str, entries0[str]); old_dent_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err, dirs, files; asynced); if dent.dentry? then vfs_put_inode#(new_dent_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)%⊦ 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)% ⊦ p + str ' ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ (p + str ').last = str; (s)