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Proof step 1 from proof intersection-shift (conclusion)

⊦ a ∈ s → s ∩ (s0 ++ a) = (s ∩ s0) ++ a

System applied rule normalize

And obtained the following new goals

Proof step 2:
a ∈ s ⊦ s ∩ (s0 ++ a) = (s ∩ s0) ++ a

Rule argument

Additional information