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Proof step 98 from proof rename-fids (previous step)

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

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] → [{fid1} , root0.fids \ {fid0} , fid] flags: <all paths>

Additional information

Used simplifier rules: ⊦ fid0 ∈ fidb ∧ fid0 ≠ fid1 → fid0 ∈ fidb \ {fid1} ; (ss)% ⊦ fid ∈ {fid0} ↔ fid = fid0; (s)% ⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0; (ws)%union-ass: ⊦ fidb ∪ fidb0 ∪ fidb1 = (fidb ∪ fidb0) ∪ fidb1; from specification bag-union[fidbag]%union-com: ⊦ fidb ∪ fidb0 = fidb0 ∪ fidb; from specification bag-union[fidbag] Used terms: {fid1} , root0.fids \ {fid0} , fid