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Proof step 5 from proof ri-closed-drop (previous step)

range ri ∩ as = ∅, key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro) ⊦ ri[key] ∈ as, ri[key] ∈ fs \ as ∧ node-closed(fs[ri[key]], ri, fs \ as, ro)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
range ri ∩ as = ∅, key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro) ⊦ ri[key] ∈ fs \ as ∧ node-closed(fs[ri[key]], ri, fs \ as, ro)

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ as ∩ range ri = ∅ → ¬ ri[key] ∈ as; (s)%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]