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Proof step 15 from proof abs-meta-h (previous step)

tree[p].dir? ↔ m ∈ dirs, (((abs|(tree, ino, p, m) * abs(tree[p], m)) * D))(dirs), ispath(p, ino, m, dirs, files), p ∈ tree, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ meta(p, tree, abs-files(files)) = meta(ε, m, dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
tree[p].dir? ⊦ meta(p, tree, fs) = tree[p].meta
Proof step 17:
tree[p].dir? ↔ m ∈ dirs, (((abs|(tree, ino, p, m) * abs(tree[p], m)) * D))(dirs), ispath(p, ino, m, dirs, files), p ∈ tree, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ meta(p, tree, abs-files(files)) = meta(ε, m, dirs, files), tree[p].dir?
Proof step 22:
tree[p].dir? ↔ m ∈ dirs, (((abs|(tree, ino, p, m) * abs(tree[p], m)) * D))(dirs), tree[p].dir?, ispath(p, ino, m, dirs, files), p ∈ tree, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ tree[p].meta = meta(ε, m, dirs, files)

Rule argument

spec: posix-base name: meta-dir seq: tree[p].dir? ⊦ meta(p, tree, fs) = tree[p].meta subst: [fs, tree, p] → [abs-files(files), tree, p] flags: <all paths>

Additional information

Used terms: abs-files(files), tree, p