NP ⊆ AM

Inclusion · folklore

Statement

$\mathbf{NP}\subseteq \mathbf{AM}$: every language in NP has an Arthur–Merlin proof system with perfect completeness and perfect soundness — folklore.

Sketch

Merlin ignores Arthur’s coins and sends an $\mathbf{NP}$ witness, which Arthur checks with the deterministic $\mathbf{NP}$ verifier, so completeness and soundness are those of that verifier.