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Proof step 11 from proof rename-fids (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
root0[path'] = fnode(fid), path' ≠ ε, root0[parent(path')].dir?, fids-cons(root0, fs, ofh), py(user, parent(path'), root0, fs), py(user, parent(path), root0, fs), parent(path') ∈ root0, path ∈ root0, path' ∈ root0, ¬ root0[path].dir?, ¬ fid ∈ ofh.fids, ¬ fid ∈ (root0 -- path)[path', root0[path]].fids, ¬ path ⊑ path' ⊦ [fs := fs -- fid; psynced := ?] fids-cons((root0 -- path)[path', root0[path]], fs, ofh)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ fnode(fid).dir?; (s)