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Proof step 10 from proof px-last (previous step)

px(user, parent(p), ino, dirs, files), px(user, meta(p, ino, dirs, files)), q ⊑ p ⊦ px(user, meta(q, ino, dirs, files))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ px(user, p, ino, dirs, files) ↔ (∀ q. q ⊑ p → px(user, meta(q, ino, dirs, files)))
Proof step 12:
px(user, meta(p, ino, dirs, files)), q ⊑ p, ∀ q. q ⊑ parent(p) → px(user, meta(q, ino, dirs, files)) ⊦ px(user, meta(q, ino, dirs, files))

Rule argument

spec: path-permission, inst: vfs-permission name: px seq: ⊦ px(user, p, ino, dirs, files) ↔ (∀ q. q ⊑ p → px(user, meta(q, ino, dirs, files))) subst: [files, dirs, ino, p, user] → [files, dirs, ino, parent(p), user] flags: <all paths>

Additional information

Used terms: files, dirs, ino, parent(p), user