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Proof step 34 from proof fids-put1 (previous step)

tree[parent(p0)].dir?, p0 ∈ tree, tree[p0].fids ⊆ tree.fids ⊦ p0 = ε, sdt0.fids ∪ ((tree.fids ∪ tree1.fids) \ tree[p0].fids) = ((sdt0.fids ∪ tree.fids) ∪ tree1.fids) \ tree[p0].fids, str ∈ sdt0, tree[p0].fids ⊆ tree.fids ∪ tree1.fids

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: bag-union, inst: fidbag name: count-subset seq: ⊦ fidb ⊆ fidb0 ↔ (∀ fid. count(fid, fidb) ≤ count(fid, fidb0)) subst: [fidb0, fidb] → [tree.fids, tree[p0].fids] flags: <all paths>

Additional information

Used terms: tree.fids, tree[p0].fids