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Given a variety V and a set of variables X, IrB(Idv(X)) is a convex set.

I need a complete proof for this theorem.

If anyone can help me it would be wonderful.

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Finally I find out the proof of the Tarski theorem. When we proof that τ(Id_v (X))=θ_FI τ(Σ), then with the lemma 14.4 we know that θ is an algebraic closure operator & is 2-ary. Know with the Tarski theorem in section 1 page 36, we can deduct that θ is a convex set.

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