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Proof step 11 from proof abs-meta-h (previous step)

tree[p].dir? ↔ m ∈ dirs, ((abs(tree, ino) * 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ p ∈ tree → abs(tree, ino0) = _∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1))
Proof step 13:
tree[p].dir? ↔ m ∈ dirs, ((_∃(λ ino1. abs|(tree, ino, p, ino1) * abs(tree[p], ino1)) * 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)

Rule argument

spec: <toplevel> name: path-unfold seq: ⊦ p ∈ tree → abs(tree, ino0) = _∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1)) subst: [p, ino0, tree] → [p, ino, tree] flags: <all paths>

Additional information

Used terms: p, ino, tree