Let me be more explicit. All the proofs Paul notes are along the lines of: Construct some types that induce irr scs and then show that all irr scs are thus obtained. In other words they are explict constructions. But that is stronger than the original question asked. One might hope that there would be a general proof that all irr scs are induced for reductive p-adic groups that doesn't produce the types.
mander
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