coNP ⊆ coAM

Inclusion · folklore

Statement

coNP $\subseteq$ coAM — folklore.

Sketch

$\mathbf{NP}\subseteq \mathbf{AM}$ via the AM protocol in which Arthur ignores his coins and accepts iff Merlin’s message is an $\mathbf{NP}$ witness (NP ⊆ AM); complementing both sides gives the claim.