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Proof step 88 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, q, ROOT_INO, dirs, files), py(user, parent(path'), root, abs-files(files)), ino1 ∈ dirs, psynced → asynced ⊦ path' = ε, px(user, md)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 89:
⊦ px(user, p, ino, dirs, files) ↔ (∀ q. q ⊑ p → px(user, meta(q, ino, dirs, files)))
Proof step 90:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), py(user, parent(path'), root, abs-files(files)), ino1 ∈ dirs, psynced → asynced, ∀ q0. q0 ⊑ q → px(user, meta(q0, ROOT_INO, dirs, files)) ⊦ path' = ε, px(user, md)

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, ROOT_INO, q, user] flags: <all paths>

Additional information

Used terms: files, dirs, ROOT_INO, q, user