Let p, q and alpha be given.

Assume Ha.

Let beta be given.

Assume Hb H1.

Let gamma be given.

Assume H2: gamma ∈ beta.

We will prove p gamma ↔ q gamma.

Apply H1 to the current goal.

We will prove gamma ∈ alpha.

Apply Ha to the current goal.

Assume Ha1 _.

An exact proof term for the current goal is Ha1 beta Hb gamma H2.

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