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Proof step 1 from proof in-uni (conclusion)

⊦ rs0 ∩ rs1 = ∅ → (r ∈ mk(rs0, f0) ∪ mk(rs1, f1) ↔ r ∈ rs0 ∨ r ∈ rs1)

System applied rule normalize

And obtained the following new goals

Proof step 2:
rs0 ∩ rs1 = ∅ ⊦ r ∈ mk(rs0, f0) ∪ mk(rs1, f1) ↔ r ∈ rs0 ∨ r ∈ rs1

Rule argument

Additional information