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Proof step 72 from proof rename-fids (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 73:
⊦ tree[p] = fnode(fid) ∧ p ∈ tree → fid ∈ tree.fids
Proof step 74:
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 ⊦ path' = ε, fid ∈ fs, fid ∈ ofh.fids, fid ∈ root0.fids, path ⊑ path', root0[path + str ' + p] = fnode(fid) ∧ path + str ' + p ∈ root0

Rule argument

spec: directory-tree-fids name: fids-path seq: ⊦ tree[p] = fnode(fid) ∧ p ∈ tree → fid ∈ tree.fids subst: [p, tree, fid] → [path + str ' + p, root0, fid] flags: <all paths>

Additional information

Used terms: path + str ' + p, root0, fid