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Proof step 34 from proof walk-prepost-h (previous step)

dirs[ino] = mkdir(m, md, # links(ino, dirs), m1, entries), err = EACCESS, p = p0, 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), ∀ 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))) ⊦ p0 = ε, px(user, md), ⌊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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
dirs[ino] = mkdir(m, md, # links(ino, dirs), m1, entries), 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))) ⊦ p0 = ε, px(user, md), ∃ p'. p' ⊑ parent(p0) ∧ ispath(p', ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ ESUCCESS ≠ EACCESS; (s)% ⊦ ENOENT ≠ EACCESS; (s)% ⊦ ¬ ⌊EACCESS⌋ ; (s)