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Proof step 18 from proof py-strong (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ tree[ε] = tree; (s)% ⊦ ispath(ε, n, m, dirs, files) ↔ valid-ino(n, dirs, files) ∧ m = n; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ px(user, ε, ino, dirs, files) ↔ px(user, meta(ε, ino, dirs, files)); (s) Used terms: files, dirs, ino, q, user