Mixed Euler number is additive on the right

For a surface with ample $A$ and line bundles $M,N,P$: $M\cdot(N\otimes P)=M\cdot N+M\cdot P$, with $\cdot$ the mixed Euler number.

Notation. $L\cdot M$ is mixedEuler, namely $\chi(L\otimes M)-\chi(L)-\chi(M)+\chi(\mathcal O_S)$. IsAmple means that for each point $x$ and open $V\ni x$, some positive power has a global section with nonvanishing open containing $x$, inside $V$, and affine. A Surface is an integral scheme smooth of relative dimension 2 over $\operatorname{Spec}\mathbb C$ with a closed immersion into some complex projective space over $\mathbb C$.

Formalization Note The statement is verbatim from OpenAI's Lean development, with Definitions files of this development imported in place of the upstream modules; these are supporting code for the statement.