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Proof step 11 from proof inv-rmdir (previous step)

asynced0 ↔ asynced, dirs0 = dirs, files0 = files, ino = ROOT_INO, p1 = p0, user0 = user, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files) ⊦ [vfs_walk#(parent(p0), user, dirs, files, asynced; ino, err)] ( (∃ q, str. p1 = 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(p0.last); if err = ESUCCESS then {isdir := true; vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), p0 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
ino = ROOT_INO, p0 ≠ ε, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files) ⊦ [vfs_walk#(parent(p0), user, dirs, files, asynced; ino, err)] ( (∃ q, str. p0 = 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(p0.last); if err = ESUCCESS then {isdir := true; vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Rule argument

Additional information

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