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Proof step 148 from proof walk-prepost-h (previous step)

dirs[entries0[str]] = mkdir(m, md, # links(entries0[str], dirs), m2, entries), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), ino = entries0[str], p = str0 ' + p0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), px(user, md0), px(user, md), ino0 ∈ dirs, entries0[str] ∈ dirs, str ∈ entries0, ⌊err0⌋ , 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 ∧ err0 = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err0); if err0 = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err0); if err0 = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err0⌋ ∨ err0 = ESUCCESS ∧ str0 ∈ entries ∧ ispath(p0, entries[str0], ino, dirs, files) ∧ px-parent(user, q + str ' + str0 ' + p0, ROOT_INO, dirs, files) ∨ err0 = ENOENT ∧ (¬ str0 ∈ entries ∨ ¬ ispath(p0, entries[str0], dirs, files)) ∨ err0 = 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)

Heuristic loop exit applied rule while exit right

And closed the goal!

Rule argument

pos: right 1

Additional information

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