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Proof step 1 from proof ri-closed-variant1-01 (conclusion)

⊦ ri-closed(ri, fs, ro) → ( ri-closed(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)))

System applied rule normalize

And obtained the following new goals

Proof step 2:
ri-closed(ri, fs, ro) ⊦ ri-closed(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))

Proof step 1 from proof ri-closed-variant1-01 (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

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