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Proof step 1 from proof put-sw-in (conclusion)

⊦ m < # x ∧ n < # x → (a ∈ x[m, x[n]][n, x[m]] ↔ a ∈ x)

System applied rule normalize

And obtained the following new goals

Proof step 2:
m < # x, n < # x ⊦ a ∈ x[m, x[n]][n, x[m]] ↔ a ∈ x

Rule argument

Additional information