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Proof step 23 from proof abs-meta-h (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
tree[p] = dnode(md, sdt), (((abs|(tree, ino, p, m) * abs(tree[p], m)) * D))(dirs), tree[p].dir?, ispath(p, ino, m, dirs, files), m ∈ dirs, p ∈ tree, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ md = dirs[m].meta

Rule argument

spec: directory-tree name: dnode-elim seq: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt) subst: [tree, md, sdt] → [tree[p], md, sdt]

Additional information

Used simplifier rules: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt); (elim) Used terms: tree[p], md, sdt