Advice elimination (Ben-David & Dichterman 1998): If C is PAC-learnable with concept-dependent advice from a FINITE set A (with measurability regularity), then C is PAC-learnable without advice.

Proof strategy: run the advice-augmented learner with each a ∈ A on a training portion of the sample, producing |A| candidate hypotheses. Use a validation portion to select the candidate with lowest empirical error. Union bound over |A| advice values + Hoeffding on validation controls total failure probability. Sample complexity: O(m_orig(ε/2, δ/(2|A|)) + log(|A|/δ)/ε²).

The [Fintype A] constraint is essential: for infinite A, the theorem is false (no finite union bound). [Nonempty A] ensures the advice space is inhabited.