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Proof step 14 from proof py-prefix (previous step)

tree[q].dir? ↔ m ∈ dirs, meta(q0, tree, abs-files(files)) = meta(q0, ino, dirs, files), abs(tree, ino)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(q, ino, m, dirs, files), pw(user, p, tree, abs-files(files)), px(user, p, tree, abs-files(files)), q0 ⊑ p, q ⊑ p, q0 ⊑ q ⊦ px(user, meta(q0, ino, dirs, files))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ px(user, p, tree, fs) ↔ (∀ q. q ⊑ p → px(user, meta(q, tree, fs)))
Proof step 16:
tree[q].dir? ↔ m ∈ dirs, meta(q0, tree, abs-files(files)) = meta(q0, ino, dirs, files), abs(tree, ino)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(q, ino, m, dirs, files), pw(user, p, tree, abs-files(files)), q0 ⊑ q, q ⊑ p, q0 ⊑ p, ∀ q. q ⊑ p → px(user, meta(q, tree, abs-files(files))) ⊦ px(user, meta(q0, ino, dirs, files))

Rule argument

spec: path-permission, inst: posix-permission name: px seq: ⊦ px(user, p, tree, fs) ↔ (∀ q. q ⊑ p → px(user, meta(q, tree, fs))) subst: [fs, tree, p, user] → [abs-files(files), tree, p, user] flags: <all paths>

Additional information

Used terms: abs-files(files), tree, p, user