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Proof step 90 from proof rename-fids (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: bag-union, inst: fidbag name: in-diff-notfirst seq: ⊦ ¬ fid ∈ fidb → ¬ fid ∈ fidb \ fidb0 subst: [fidb0, fidb, fid] → [(path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path) ;fnode(fid1) ) .fids, root0.fids \ {fid0} , fid] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ fid ∈ fidb → ¬ fid ∈ fidb \ fidb0; (s) Used terms: (path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path);fnode(fid1)).fids, root0.fids \ {fid0} , fid