| afs-cons(dirs, files), ispath(q, ROOT_INO, ino, dirs, files), ino ∈ dirs, q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files), ∀ p1, err, p, p_ino, ino, dirs, files, q, user, asynced. # p1 < # p0 → err = ESUCCESS ∧ p = p1 ∧ p_ino = ino ∧ afs-cons(dirs, files) ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ (q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files)) → [while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p1, p_ino, ino, dirs, files) ∧ px-parent(user, q + p1, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p1, p_ino, dirs, files) ∨ err = EACCESS ∧ p1 ≠ ε ∧ (∃ p'. p' ⊑ parent(p1) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))) ⊦ [choose err0 with ⌊err0⌋ in err := err0; if err = ESUCCESS then if ¬ inode.directory then err := ENOENT else if ¬ px(user, inode.meta) then err := EACCESS; p_ino := ino; p := p0; if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}; while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p0, p_ino, ino, dirs, files) ∧ px-parent(user, q + p0, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p0, p_ino, dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ parent(p0) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))), p0 = ε |
afs-cons(dirs, files), ispath(q, ROOT_INO, ino, dirs, files), ino ∈ dirs, ⌊err0⌋ , q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files), ∀ p1, err, p, p_ino, ino, dirs, files, q, user, asynced. # p1 < # p0 → err = ESUCCESS ∧ p = p1 ∧ p_ino = ino ∧ afs-cons(dirs, files) ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ (q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files)) → [while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p1, p_ino, ino, dirs, files) ∧ px-parent(user, q + p1, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p1, p_ino, dirs, files) ∨ err = EACCESS ∧ p1 ≠ ε ∧ (∃ p'. p' ⊑ parent(p1) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))) ⊦ [err := err0; if err = ESUCCESS then if ¬ inode.directory then err := ENOENT else if ¬ px(user, inode.meta) then err := EACCESS; p_ino := ino; p := p0; if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}; while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p0, p_ino, ino, dirs, files) ∧ px-parent(user, q + p0, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p0, p_ino, dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ parent(p0) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))), p0 = ε