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Proof step 1 from proof walk-prepost (conclusion)

ino = ROOT_INO, afs-cons(dirs, files) ⊦ ⟪vfs_walk#(p, user, dirs, files, asynced; ino, err)⟫ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p, ROOT_INO, ino, dirs, files) ∧ px-parent(user, p, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ p ≠ ε ∧ (∃ p'. p' ⊑ parent(p) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)))

User applied rule insert program lemma

And obtained the following new goals

Proof step 2:
ino ∈ dirs, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, afs-cons(dirs, files) ⊦ ⟪vfs_walk#(p, user, dirs, files, asynced; ino, err)⟫ true
Proof step 3:
asynced0 ↔ asynced, dirs0 = dirs, files0 = files, ino = ROOT_INO, p0 = p, user0 = user, afs-cons(dirs, files), ino ∈ dirs, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ [vfs_walk#(p, user, dirs, files, asynced; ino, err)] ( true → ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p, ROOT_INO, ino, dirs, files) ∧ px-parent(user, p, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ p ≠ ε ∧ (∃ p'. p' ⊑ parent(p) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)))

Rule argument

spec: <toplevel> name: walk-term seq: ino ∈ dirs, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, afs-cons(dirs, files) ⊦ ⟪vfs_walk#(p, user, dirs, files, asynced; ino, err)⟫ true subst: [asynced, files, dirs, user, p, err, ino] → [asynced, files, dirs, user, p, err, ino] flags: <all paths>

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)