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Proof step 22 from proof inv-unlink (previous step)

root0[path] = fnode(fid), path ≠ ε, root0.dir?, fids-cons(root0, fs, ofh), py(user, parent(path), root0, fs), path ∈ root0 ⊦ ⟪psynced := ?⟫ fids-cons(root0 -- path, fs, ofh), ¬ fid ∈ ofh.fids ∧ ¬ fid ∈ root0.fids \ {fid}

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ fid ∈ fidb ∧ ¬ fid ∈ fidb0 → (fid ∈ fidb \ fidb0 ↔ true)
Proof step 24:
root0[path] = fnode(fid), root0.dir?, fids-cons(root0, fs, ofh), py(user, parent(path), root0, fs), path ∈ root0 ⊦ ⟪psynced := ?⟫ fids-cons(root0 -- path, fs, ofh), path = ε, ¬ fid ∈ ofh.fids ∧ ¬ fid ∈ root0.fids \ {fid} , fid ∈ root0.fids ∧ ¬ fid ∈ {fid}

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, fid] flags: <all paths>

Additional information

Used simplifier rules: ⊦ fid ∈ {fid0} ↔ fid = fid0; (s) Used terms: {fid} , root0.fids, fid