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Proof step 1 from proof disj-singleton-write (conclusion)

r ≠ null ⊦ (∅ ++ r)[r, o] ⊥ H ↔ ¬ r ∈ H

System applied rule normalize

And obtained the following new goals

Proof step 2:
⊦ (∅ ++ r)[r, o] ⊥ H ↔ ¬ r ∈ H, r = null

Rule argument

Additional information