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Proof step 25 from proof fids-put1 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: directory-tree name: put-rec seq: p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]]) subst: [tree0, p, str, sdt, md] → [tree1, p0, str, sdt0[str, tree], md] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ∈ sdt[str, tree]; (s) Used terms: tree1, p0, str, sdt0[str, tree], md