[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 977 from proof inv-renam (previous step)

files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], dirs), content), dirs[ino] = mkdir(m, md, # links(ino, dirs), m2, entries), dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), err = ESUCCESS, p_inode = mkinode(entries0[str], md1, false, # links(entries0[str], dirs), 0, m1), 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, md0), pw(user, md), px(user, md), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ files, ino ∈ dirs, str0 ∈ entries, ¬ entries0[str] ∈ dirs, ¬ q + str ' ⊑ q0 + str0 ', links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪afs_iget#(mkdentry(str0, entries[str0]).ino, dirs, files, asynced; p_inode, err); isdir := false; if err = ESUCCESS then {isdir := p_inode.directory; if isdir then if p_inode.ino = ROOT_INO then err := EACCESS else if p_inode.size ≠ 0 then err := ENOTEMPTY}; isdir0 := isdir; isdir := false; if isdir ∧ ¬ isdir0 then err := ENOTDIR; if ¬ isdir ∧ isdir0 then err := EISDIR; new_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) ); new_dent := mkdentry(mkdentry(str0, entries[str0]).name, dirs[ino].entries[mkdentry(str0, entries[str0]).name]); 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 978:
dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), dirs[ino] = mkdir(m, md, # links(ino, dirs), m2, entries), files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], dirs), content), dirs[ino] = mkdir(m4, md2, m5, m6, entries1), err = ESUCCESS, p_inode = mkinode(entries0[str], md1, false, # links(entries0[str], dirs), 0, m1), dom of < ino2, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), ispath(q0, ROOT_INO, ino, dirs, files), of-cons(of, dirs, files), pw(user, md), pw(user, md0), px(user, md0), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), str0 ∈ entries, ino ∈ dirs, entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪afs_iget#(mkdentry(str0, entries[str0]).ino, dirs, files, asynced; p_inode, err); isdir := false; if err = ESUCCESS then {isdir := p_inode.directory; if isdir then if p_inode.ino = ROOT_INO then err := EACCESS else if p_inode.size ≠ 0 then err := ENOTEMPTY}; isdir0 := isdir; isdir := false; if isdir ∧ ¬ isdir0 then err := ENOTDIR; if ¬ isdir ∧ isdir0 then err := EISDIR; new_inode := (ino ∈ dirs ⊃ mkinode(ino, md2, true, m5, m6, m4);mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size)); new_dent := mkdentry(mkdentry(str0, entries[str0]).name, entries1[mkdentry(str0, entries[str0]).name]); 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)), entries0[str] ∈ dirs, q + str ' ⊑ q0 + str0 '

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[ino], m4, md2, m5, m6, entries1]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[ino], m4, md2, m5, m6, entries1