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Proof step 60 from proof walk-prepost-h (previous step)

dirs[ino0] = mkdir(m, md, # links(ino0, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, err0 = ESUCCESS, ino = mkdentry(dent.name, dirs[p_ino].entries[dent.name]).ino, p = p0.tail, p0 = str ' + p2, p_ino = ino0, p_ino0 = ino0, mkdentry(dent.name, dirs[p_ino].entries[dent.name]).dentry?, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), pre-lookup(p_ino, dent, dirs, files), px(user, md), dent.name ∈ dirs[p_ino].entries, ino0 ∈ dirs, q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files), ∀ p1, err, p, p_ino, ino, dirs, files, q, user, asynced. # p1 < #(str + p2) → 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 ∧ p_ino0 ∈ dirs ∧ str ∈ dirs[p_ino0].entries ∧ ispath(p2, dirs[p_ino0].entries[str], ino, dirs, files) ∧ px-parent(user, q + str ' + p2, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ (¬ p_ino0 ∈ dirs ∨ ¬ str ∈ dirs[p_ino0].entries ∨ ¬ ispath(p2, dirs[p_ino0].entries[str], dirs, files)) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ parent(str ' + p2) ∧ ispath(p', p_ino0, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))), p0 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
dirs[ino0] = mkdir(m, md, # links(ino0, dirs), m1, entries), err = ESUCCESS, ino = entries[str], p = p2, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), px(user, md), ino0 ∈ dirs, str ∈ 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 + p2) → 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 ∧ ispath(p2, dirs[ino0].entries[str], ino, dirs, files) ∧ px-parent(user, q + str ' + p2, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p2, dirs[ino0].entries[str], dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ parent(str ' + p2) ∧ ispath(p', ino0, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)% ⊦ str ' + p ≠ ε; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ negdentry(str).name = str; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ (str ' + p).tail = p; (s)