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Proof step 137 from proof walk-prepost-h (previous step)

dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), dirs[entries0[str]] = mkdir(m, md, # links(entries0[str], dirs), m2, entries), dent = negdentry(str0), err = ENOENT, err0 = ESUCCESS, ino = entries0[str], p = str0 ' + p0, p_ino = entries0[str], afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), px(user, md), px(user, md0), entries0[str] ∈ dirs, ino0 ∈ dirs, str ∈ entries0, q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files), links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, ∀ p1, err, p, p_ino, ino, dirs, files, q, user, asynced. # p1 < #(str + str0 + 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))) ⊦ [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 ∧ str0 ∈ entries ∧ ispath(p0, entries[str0], ino, dirs, files) ∧ px-parent(user, q + str ' + str0 ' + p0, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ (¬ str0 ∈ entries ∨ ¬ ispath(p0, entries[str0], dirs, files)) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ str ' + parent(str0 ' + p0) ∧ ispath(p', ino0, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))), dent.name ∈ dirs[p_ino].entries, ispath(q + str ', ROOT_INO, entries0[str], dirs, files) ∧ px(user, q, ROOT_INO, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 138:
dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), dirs[entries0[str]] = mkdir(m, md, # links(entries0[str], dirs), m2, entries), err = ENOENT, ino = entries0[str], p = str0 ' + p0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), px(user, md), px(user, md0), entries0[str] ∈ dirs, ino0 ∈ dirs, str ∈ entries0, ¬ str0 ∈ entries, q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files), links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, ∀ p1, err, p, p_ino, ino, dirs, files, q, user, asynced. # p1 < #(str + str0 + 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))) ⊦ [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 = ENOENT ∨ err = EACCESS ∧ (∃ p'. p' ⊑ str ' + parent(str0 ' + p0) ∧ ispath(p', ino0, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))), ispath(q + str ', ROOT_INO, entries0[str], dirs, files) ∧ px(user, q, ROOT_INO, dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ str ∈ str0 ' + p ↔ str = str0 ∨ str ∈ p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]%in-14: ⊦ str ' + p = p0 → str ∈ p0; (forward) from specification list[path]% ⊦ negdentry(str).name = str; (s)