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Proof step 17 from proof inv-link (previous step)

fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ ofh.fids, root[path] = fnode(fid), root.dir?, root[parent(path')].dir?, fids-cons(root, fs, ofh), px(user, parent(path), root, fs), py(user, parent(path'), root, fs), path ∈ root, parent(path') ∈ root ⊦ fid0 ∈ fs ↔ (fid0 ∈ root.fids ∨ fid0 ∈ {fid} ) ∨ fid0 ∈ ofh.fids, path' ∈ root

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ ofh.fids, root[path] = fnode(fid), root[parent(path')].dir?, root.dir?, fids-cons(root, fs, ofh), px(user, parent(path), root, fs), py(user, parent(path'), root, fs), parent(path') ∈ root, path ∈ root ⊦ fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 = fid ∨ fid0 ∈ ofh.fids, path' ∈ root

Rule argument

Additional information

Used simplifier rules: ⊦ fid ∈ {fid0} ↔ fid = fid0; (s)