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Proof step 83 from proof rename-fids (previous step)

fid ∈ fs ↔ fid ∈ root0.fids ∨ fid ∈ ofh.fids, fnode(fid0) = root0[path], root0[parent(path')].dir?, (root0 -- path)[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 ⊦ fid ∈ fs ↔ fid ∈ ((root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ root0[path'] -- restn(# path', path);root0[path']).fids) ∪ {fid0} ∨ fid ∈ ofh.fids, path' = ε, root0[path'].dir?, path ⊑ path', ¬ root0[path'].fid ∈ ofh.fids ∧ ¬ root0[path'].fid ∈ ((root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ root0[path'] -- restn(# path', path);root0[path']).fids) ∪ {fid0}

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 84:
fid ∈ fs ↔ fid ∈ root0.fids ∨ fid ∈ ofh.fids, root0[path'] = fnode(fid1), fnode(fid0) = root0[path], (root0 -- path)[parent(path')].dir?, 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 ⊦ fid ∈ fs ↔ fid ∈ ((root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ root0[path'] -- restn(# path', path);root0[path']).fids) ∪ {fid0} ∨ fid ∈ ofh.fids, path' = ε, root0[path'].dir?, path ⊑ path', ¬ fid1 ∈ ofh.fids ∧ ¬ fid1 ∈ ((root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ root0[path'] -- restn(# path', path);root0[path']).fids) ∪ {fid0}

Rule argument

spec: directory-tree name: fnode-elim seq: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid) subst: [tree, fid] → [root0[path'], fid1]

Additional information

Used simplifier rules: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid); (elim) Used terms: root0[path'], fid1