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Proof step 1 from proof subseteq-union-simp (conclusion)

⊦ as = as0 ∪ as1 → (as ⊆ as0 ∪ as2 ↔ as1 ⊆ as0 ∪ as2)

System applied rule normalize

And obtained the following new goals

Proof step 2:
as = as0 ∪ as1 ⊦ as ⊆ as0 ∪ as2 ↔ as1 ⊆ as0 ∪ as2

Rule argument

Additional information