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Proof step 3 from proof ri-closed-variant1-01 (previous step)

∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro) ⊦ (∀ key. key ∈ ri0 → ri0[key] ∈ fs0 ∧ node-closed(fs0[ri0[key]], ri0, fs0, ro0)) ↔ (∀ key. (key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro)) → key ∈ ri0 → ri0[key] ∈ fs0 ∧ node-closed(fs0[ri0[key]], ri0, fs0, ro0))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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