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Proof step 2 from proof ri-closed-drop (previous step)

range ri ∩ as = ∅, ri-closed(ri, fs, ro) ⊦ ri-closed(ri, fs \ as, ro)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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 \ as)[ri[key]], ri, fs \ as, ro)

Rule argument

Additional information

Used simplifier rules: ri-closed: ⊦ ri-closed(ri, fs, ro) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro));