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Proof step 40 from proof rename-fids (previous step)

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'

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: bag-union, inst: fidbag name: differente-notin seq: ⊦ fid ∈ fidb ∧ ¬ fid ∈ fidb0 → (fid ∈ fidb \ fidb0 ↔ true) subst: [fidb0, fidb, fid] → [{fid} , root0.fids \ {fid1} , fid0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ fid0 ∈ fidb ∧ fid0 ≠ fid1 → fid0 ∈ fidb \ {fid1} ; (ss)% ⊦ fid ∈ {fid0} ↔ fid = fid0; (s) Used terms: {fid} , root0.fids \ {fid1} , fid0