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Proof step 75 from proof rename-fids (previous step)

root0[path'] = dnode(md0, ∅), sdt[str][p] = fnode(fid), dnode(md, sdt) = root0[path], (root0 -- path)[parent(path')].dir?, root0[parent(path')].dir?, fids-cons(root0, fs, ofh), pw(user, path, root0, fs), py(user, parent(path), root0, fs), py(user, parent(path'), root0, fs), path' ∈ root0, path ∈ root0, parent(path') ∈ root0, p ∈ sdt[str], str ∈ sdt ⊦ root0[path + str ' + p] = fnode(fid), path' = ε, fid ∈ fs, fid ∈ ofh.fids, fid ∈ root0.fids, path ⊑ path'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 76:
⊦ p ∈ tree → tree[p + q] = tree[p][q]

Rule argument

spec: directory-tree name: split-at seq: ⊦ p ∈ tree → tree[p + q] = tree[p][q] subst: [q, p, tree] → [str ' + p, path, root0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p] = sdt[str][p]; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path] Used terms: str ' + p, path, root0