= Solution
The first correction to the four-point coupling containing $\lambda_0$ is of order $\lambda_0^2$: two cubic vertices are joined by one fast internal propagator, leaving four slow external legs. The three exchange channels pair the external legs in the $s$, $t$, and $u$ ways. In a sharp momentum-shell scheme this contribution is retained when the exchanged momentum lies in the eliminated shell; its derivative expansion supplies the induced local quartic interaction.
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