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Proof step 27 from proof refine-link (previous step)

asynced0 ↔ asynced, dirs0 = dirs, err = err0, files0 = files, ino = ROOT_INO, p0 = path0, user0 = user, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ [vfs_walk#(parent(path0), 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(path0.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(path'.last), path = parent(path') in {vfs_walk#(path, 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); fs := abs-files(files); 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) → ⟨posix_link#(path0, path', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))), path' = ε, path0 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
err = err0, ino = ROOT_INO, path' ≠ ε, path0 ≠ ε, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ [vfs_walk#(parent(path0), user, dirs, files, asynced; ino, err)] ( (∃ q, str. path0 = 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(path0.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(path'.last), path = parent(path') in {vfs_walk#(path, 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); fs := abs-files(files); 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) → ⟨posix_link#(path0, path', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0)))

Rule argument

Additional information

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