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Proof step 11 from proof inv-link (previous step)

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 ⊦ ⟪psynced := ?⟫ fids-cons(root[path', fnode(fid)], fs, ofh), root[path].dir?, path' ∈ root

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
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, ¬ path' ∈ root ⊦ ⟪psynced := ?⟫ fids-cons(root[path', fnode(fid)], fs, ofh)

Rule argument

Additional information

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