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Proof step 10 from proof rename-fids (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
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'

Rule argument

spec: directory-tree name: fnode-elim seq: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid) subst: [tree, fid] → [root0[path'], fid]

Additional information

Used simplifier rules: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid); (elim) Used terms: root0[path'], fid