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Proof step 12 from proof inv-link (previous step)

asynced0 ↔ asynced, dirs0 = dirs, files0 = files, ino = ROOT_INO, p0 = p3, user0 = user, afs-cons(dirs, files), of-cons(of, dirs, files) ⊦ [vfs_walk#(parent(p3), user, dirs, files, asynced; ino, err)] ( (∃ q, str. p0 = q + str ∧ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q, ROOT_INO, ino, dirs0, files0) ∧ px-parent(user0, q, ROOT_INO, dirs0, files0) ∨ err = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs0, files0) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ q ∧ ispath(p', ROOT_INO, dirs0, files0) ∧ ¬ px(user0, p', ROOT_INO, dirs0, files0)))) → ⟪dent := negdentry(p3.last); if err = ESUCCESS then vfs_may_link#(ino, user, dirs, files, asynced; inode, dent, err); c_inode := inode; old_dent := dent; if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), p = ε, p3 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
ino = ROOT_INO, p ≠ ε, p3 ≠ ε, afs-cons(dirs, files), of-cons(of, dirs, files) ⊦ [vfs_walk#(parent(p3), user, dirs, files, asynced; ino, err)] ( (∃ q, str. p3 = q + str ' ∧ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)))) → ⟪dent := negdentry(p3.last); if err = ESUCCESS then vfs_may_link#(ino, user, dirs, files, asynced; inode, dent, err); c_inode := inode; old_dent := dent; if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Rule argument

Additional information

Used simplifier rules: ⊦ p + str = p + str '; (s)