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Proof step 16 from proof rename-root (previous step)

root0[path'] = fnode(fid), root0[parent(path')].dir?, root0.dir?, py(user, parent(path'), root0, fs), py(user, parent(path), root0, fs), parent(path') ∈ root0, path ∈ root0, path' ∈ root0 ⊦ path' = ε, root0[path].dir?, (root0 -- path)[path', root0[path]].dir?, fid ∈ ofh.fids, fid ∈ (root0 -- path)[path', root0[path]].fids, path ⊑ path', path' ≠ ε ∧ (root0 -- path).dir? ∧ parent(path') ∈ root0 -- path

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
root0[path'] = fnode(fid), root0.dir?, root0[parent(path')].dir?, py(user, parent(path), root0, fs), py(user, parent(path'), root0, fs), path' ∈ root0, path ∈ root0, parent(path') ∈ root0, path ⊑ parent(path') ⊦ path' = ε, (root0 -- path)[path', root0[path]].dir?, root0[path].dir?, fid ∈ (root0 -- path)[path', root0[path]].fids, fid ∈ ofh.fids, path ⊑ path'

Rule argument

Additional information

Used simplifier rules: p ≠ ε ⊦ p ∈ tree → (q ∈ tree -- p ↔ ¬ p ⊑ q ∧ q ∈ tree); (s)%p ≠ ε ⊦ p ∈ tree → ((tree -- p).dir? ↔ tree.dir?); (s)% ⊦ p ≠ ε → (parent(p) = ε ↔ p = p.head '); (s)% ⊦ ¬ tree.dir? → (p ∈ tree ↔ p = ε); (s)% ⊦ tree[ε] = tree; (s)% ⊦ ε ∈ tree; (s)