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Proof step 1 from proof union-left-singleton (conclusion)

r ≠ null ⊦ r ∈ H → (∅ ++ r)[r, H[r]] ∪ (H -- r) = H

System applied rule normalize

And obtained the following new goals

Proof step 2:
r ∈ H ⊦ r = null, (∅ ++ r)[r, H[r]] ∪ (H -- r) = H

Rule argument

Additional information