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Proof step 13 from proof inv-renam (previous step)

ino = ROOT_INO, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files) ⊦ ∀ 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 let isrename = true in vfs_may_delete#(ino, isrename, user, dirs, files, asynced; inode, dent, p_inode, isdir, err); old_inode := inode; old_dent := dent; old_dent_inode := p_inode; 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_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ENOENT then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err) else if err = ESUCCESS then vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}; new_inode := inode; new_dent := dent; 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 {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)), p = ε, p3 = ε, p3 ⊑ p

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
p ≠ ε, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), ¬ q + str ' ⊑ p, ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q, ROOT_INO, ino1, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ ⟪dent := negdentry((q + str ').last); if err = ESUCCESS then let isrename = true in vfs_may_delete#(ino1, isrename, user, dirs, files, asynced; inode, dent, p_inode, isdir, err); old_inode := inode; old_dent := dent; old_dent_inode := p_inode; 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_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ENOENT then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err) else if err = ESUCCESS then vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}; new_inode := inode; new_dent := dent; 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 {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))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + str ' ≠ ε; (s)