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Proof step 86 from proof walk-prepost-h (previous step)

dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), ispath(p2, entries0[str], dirs, files), px(user, md0), ino0 ∈ dirs, str ∈ entries0, entries0[str] ∈ files, 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))) ⊦ p2 = ε, entries0[str] ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: afs-base name: expath seq: ⊦ ispath(p, n, dirs, files) ↔ (∃ m. ispath(p, n, m, dirs, files)) subst: [files, dirs, n, p] → [files, dirs, entries0[str], p2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ files ∧ afs-cons(dirs, files) → (ispath(p, n, m, dirs, files) ↔ n = m ∧ p = ε); (s) Used terms: files, dirs, entries0[str], p2