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Proof step 11 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), py(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 12:
⊦ py(user, p, tree, fs) ↔ pw(user, p, tree, fs) ∧ px(user, p, tree, fs)
Proof step 13:
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 ⊑ q, q ⊑ p, q0 ⊑ p ⊦ px(user, meta(q0, ino, dirs, files))

Rule argument

spec: path-permission, inst: posix-permission name: py seq: ⊦ py(user, p, tree, fs) ↔ pw(user, p, tree, fs) ∧ px(user, p, 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