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Proof step 52 from proof walk-prepost-h (previous step)

dirs[ino] = mkdir(m, md, # links(ino, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, p_ino = ino, afs-cons(dirs, files), ispath(q, ROOT_INO, ino, dirs, files), pre-lookup(p_ino, dent, dirs, files), px(user, md), ino ∈ 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))) ⊦ [if dent.name ∈ dirs[p_ino].entries then {dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}; p_ino := ino; p := str ' + p2; if err = ESUCCESS then {ino := dent.ino; p := p.tail}; 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_ino ∈ dirs ∧ str ∈ dirs[p_ino].entries ∧ ispath(p2, dirs[p_ino].entries[str], ino, dirs, files) ∧ px-parent(user, q + str ' + p2, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ (¬ p_ino ∈ dirs ∨ ¬ str ∈ dirs[p_ino].entries ∨ ¬ ispath(p2, dirs[p_ino].entries[str], dirs, files)) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ parent(str ' + p2) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files)))

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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