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Proof step 7 from proof px (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ px(user, p, ino, dirs, files) ↔ (∀ q. q ⊑ p → px(user, meta(q, ino, dirs, files)))
Proof step 9:
tree[p].dir? ↔ m ∈ dirs, abs(tree, ino)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ino, m, dirs, files) ⊦ (∀ q. q ⊑ p → px(user, meta(q, tree, abs-files(files)))) ↔ (∀ q. q ⊑ p → 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, p, user] flags: <all paths>

Additional information

Used terms: files, dirs, ino, p, user