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Proof step 39 from proof rename-fids (previous step)

root0[path'] = fnode(fid), fnode(fid1) = 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), fid0 ∈ root0.fids, path' ∈ root0, path ∈ root0, parent(path') ∈ root0, fid0 ∈ fs ⊦ fid = fid1, fid0 = fid, fid0 = fid1, path' = ε, fid0 ∈ ofh.fids, fid0 ∈ (root0.fids \ {fid1} ) \ (path' ⊑ path ⊃ fnode(fid) -- restn(# path', path);fnode(fid)).fids, fid ∈ ofh.fids, fid ∈ (root0.fids \ {fid1} ) \ fnode(fid).fids, path ⊑ path', path' ⊑ path

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
root0[path'] = fnode(fid), fnode(fid1) = 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), fid0 ∈ fs, parent(path') ∈ root0, path ∈ root0, path' ∈ root0, fid0 ∈ root0.fids ⊦ fid = fid1, fid0 = fid1, fid0 = fid, path' = ε, fid0 ∈ ofh.fids, fid ∈ (root0.fids \ {fid1} ) \ {fid} , fid ∈ ofh.fids, fid0 ∈ (root0.fids \ {fid1} ) \ {fid} , path' ⊑ path, path ⊑ path'

Rule argument

Additional information

Used simplifier rules: ⊦ fnode(fid).fids = {fid} ; (s)